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กำหนดเชิงเส้น

Published by kajankew135, 2021-04-28 04:12:03

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     ⌦        ⌦   ⌫       ⌦   ⌫ ⌦ 

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10 ⌫ ⌫  ⌦  ⌫      Á°„­µ¦ž¦³„°„µ¦Á¦¸¥œšÉ¸ 4 „µ¦Â„žo { ®µÃ‹š¥rĜ„µÎ ®œ—„µ¦ÁŠ· Á­oœ „µ¦Â„žo { ®µÃ‹š¥ršÉĸ „o µÎ ®œ—„µ¦Á·ŠÁ­œo ĜÁºÊ°Š˜œo č„o ¦µ¢Äœ„µ¦Â„žo { ®µ —Š´ œÊ´œ‹µ„Ëš¥r ž{®µ ‹Š¹ ˜°o Š­¦oµŠÂ‹Îµ¨°ŠšµŠ‡–·˜«µ­˜¦r ¨³œÎµÅžÁ…¥¸ œ„¦µ¢ „µ¦­¦µo ŠÂ‹Îµ¨°ŠšµŠ‡–˜· «µ­˜¦r ¨³ ®µ‡Îµ˜°…°Š„µÎ ®œ—„µ¦ÁŠ· Á­oœ ˜´ª°¥nµŠ 把µœÂ®nŠ®œÉŠ¹ Ÿ¨·˜­œ· ‡µo °°„¤µ 2 œ—· œ·— A ¨³ œ—· B ˜n¨³œ·Ê …°Š­·œ‡µo œ·— A ˜°o ŠŸ¨˜· —ªo ¥Á‡¦Éº°Š‹„´ ¦Ážœ} Áª¨µ 1 ª´É äŠ ®¨´Š‹µ„œœÊ´ ˜°o ŠœµÎ ¤µ˜„˜Šn —ªo ¥¤º° Áž}œÁª¨µ 2 ´ªÉ äŠ ˜n™µo œµÎ Á‡¦°Éº Š‹„´ ¦œÊœ´ ¤µŸ¨˜· ­œ· ‡oµœ·— B ˜°o ŠŸ¨·˜—oª¥Á‡¦ºÉ°Š‹´„¦Ážœ} Áª¨µ 1.5 ªÉ´ äŠ ®¨Š´ ‹µ„œœÊ´ ˜o°ŠœÎµ¤µ ˜„˜Šn —ªo ¥¤°º ץčo µn Š»—Á—¸¥ª„œ´ Ážœ} Áª¨µ 1 ´ªÉ äŠ ™oµÄœÂ˜n¨³ªœ´ Á‡¦ºÉ°Š‹„´ ¦ ¨³ ‡œ šš¸É 宜µo š¸É˜„˜nŠ šÎµŠµœª´œ¨³ 8 É´ªÃ¤Š ­·œ‡µo A ŗo„µÎ Ŧ·Êœ¨³ 300 µš ­·œ‡µo B ŗ„o εŦœ·Ê ¨³ 400 µš ™µo ˜°o Š„µ¦„µÎ Ŧ‹µ„„µ¦Ÿ¨·˜­œ· ‡µo 2 œ—· ¤µ„š­É¸ —» ‡ª¦Ÿ¨˜· ­œ· ‡µo œ—· ¨³„¸ÉœÊ· ˜°n ªœ´ ª·›¸šÎµ Ä®o Ÿ¨·˜­·œ‡µo A ªœ´ ¨³ x œÊ· Ÿ¨˜· ­·œ‡oµ B ªœ´ ¨³ y Ê·œ ¦µ¥„µ¦ ­·œ‡µo œ·— A ­·œ‡oµ…œ·— B Áª¨µš¸šÉ 劵œ (¤./ª´œ) ‹µÎ œªœ·œÊ x y Áª¨µšÉ¸ÄÁo ‡¦É°º Š‹´„¦Ÿ¨˜· (¤./·œÊ ) Áª¨µš¸É˜„˜nŠ—oª¥¤°º (¤./·œÊ ) „εŦ (µš/Êœ· ) Ä®o P Ážœ} „εŦš¸É˜o°Š„µ¦ ¨³­·œ‡µo œ—· A ¤„¸ εŦ ……. µš ­·œ‡µo œ—· B ¤¸„µÎ Ŧ …….. µš —´Šœ´œÊ ­¤„µ¦‹—» ž¦³­Š‡r ‡º° P = ……………………………. Áª¨µšÄɸ oĜ„µ¦Ÿ¨˜· ­œ· ‡µo —oª¥Á‡¦°ºÉ Š‹„´ ¦ .............. čÁo ª¨µÅ¤Án „·œ ……. É´ªÃ¤Š Áª¨µšÄɸ oĜ„µ¦˜„˜nŠ­œ· ‡oµ—ªo ¥¤°º ……….. čÁo ª¨µÅ¤Án „œ· ……. Éª´ äŠ x ¨³ y Ážœ} ‹µÎ œªœ·œÊ ­·œ‡oµš¸ŸÉ ¨·˜ x ,y Áž}œ‹µÎ œªœÁ˜È¤ª„ —Š´ œœÊ´ °­¤„µ¦…°o ‹µÎ „—´ ………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………. ……………………………………………………………………………………………………………….

⌦ 11 ⌦ ‹µ„„¦µ¢…°Š°­¤„µ¦…°o ‹Îµ„—´ ¤‹¸ »— ¤»¤…°Š¦ž¼ —´ŠœÊ¸ .......................................................... C Á„·—‹µ„Á­oœ 2x + y = 8 ˜—´ „´ x + 1.5y = 8 ŗo C (2,4) šœ‡µn x , y —oª¥¡·„—´ …°Š‹—» ¤¤» Ĝ P = 300x + 400y P= ‹»—¤¤» ‹³Å—„o µÎ Ŧ¤µ„š¸É­—» Á¤É°º Ÿ¨·˜œ—· A ‹µÎ œªœ .......... Êœ· œ·— B ‹µÎ œªœ ……..Êœ· ˜n°ª´œ

12 ⌫ ⌫  ⌦  ⌫      ˜´ª°¥µn Š Ĝ„µ¦¦„´ ¬µŸžo¼ ªi ¥ šÉ¸…µ—ª˜· µ¤œ· A ¨³ B Ÿ¼žo ªi ¥‹µÎ Áž}œ˜o°ŠÅ—o¦´ ª·˜µ¤·œ A °¥nµŠœ°o ¥ 12 „¦´¤ ª·˜µ¤·œ B °¥nµŠœo°¥ 14 „¦´¤ ŽÉŠ¹ ª·˜µ¤œ· š´ÊŠ 2 œ·—œÊ¸ ‹³Å—o ¤µ‹µ„°µ®µ¦ 2 œ—· œ·—¦„ ¤¸ª·˜µ¤œ· A ‹µÎ œªœ 2 „¦¤´ ¨³ª˜· µ¤œ· B ‹µÎ œªœ 2 „¦´¤ ˜°n °µ®µ¦ 1 œ·Ê œ·—šÉ¸ 2 ¤ª¸ ·˜µ¤œ· A ‹µÎ œªœ 1 „¦¤´ ª˜· µ¤œ· B ‹Îµœªœ 3 „¦´¤ ˜n°°µ®µ¦ 1 œ·Ê ™oµ°µ®µ¦œ—· ¦„ …µ¥œÊ· ¨³ 12.80 µš œ·—šÉ¸ 2 …µ¥Ê·œ¨³ 11.20 µš Ÿož¼ ªi ¥‡ª¦‹³Äo°µ®µ¦Â˜¨n ³œ—· Ážœ} ‹Îµœªœ„ɍ¸ œ·Ê ‹¹Š‹³šÎµÄ®Áo ­¸¥‡µn °µ®µ¦ œ°o ¥šÉ­¸ —» ª·›š¸ µÎ čo°µ®µ¦ (·Êœ) ª·˜µ¤·œ A („¦¤´ /·Êœ) ª·˜µ¤·œ B („¦´¤ / œÊ· ) ¦µ‡µ…µ¥(µš/Ê·œ) x °¥nµŠœo°¥ 14 „¦´¤ œ·—š¸É 1 œ—· š¸É 2 y ‹³˜°o ŠÄo °¥nµŠœ°o ¥ 12 „¦¤´ ­¤„µ¦‹»—ž¦³­Š‡r …………………………………………………………………………………….......... °­¤„µ¦…°o ‹µÎ „´—.............................................................................................................................................. ‹—» ¤»¤šÉŸ —‹o µ„„¦µ¢…°Š°­¤„µ¦…o°‹Îµ„´—‡º° ................................................................................................. …………......................................................................................................................................................... šœ‡nµ…°Š‹»—¤»¤…oµŠ˜oœ Ĝ­¤„µ¦‹—» ž¦³­Š‡r ‹³Å—o‡nµ P —´ŠœÊ¸ ? ‹³˜o°ŠÄo°µ®µ¦œ—· šÉ¸ 1 ‹Îµœªœ ……. Êœ· œ—· šÉ¸ 2 ‹µÎ œªœ …….. ·Êœ

⌦ 13 ⌦ ˜´ª°¥µn Š ¦·¬š´ Ÿ¨·˜£–´ ”Ár ‡¦°Éº ŠÂ˜Šn „µ¥ ˜°o Š„µ¦Ÿ¨˜· Á­°ºÊ ¨³„µŠÁ„Š Ĝ„µ¦Ÿ¨·˜Á­ºÊ° 1 ˜´ª ˜o°Š„µ¦ÄoŸoµ¨µ¥ 10 ˜µ¦µŠ¢»˜ ¨³ čŸo oµ­¸¡Êºœ 2 ˜µ¦µŠ¢˜» Á¤°Éº …µ¥‹³Å—„o εŦ˜ª´ ¨³ 30 µš Ĝ„µ¦Ÿ¨˜· „µŠÁ„Š 1 ˜ª´ ˜°o ŠÄoŸµo ¨µ¥ 4 ˜µ¦µŠ¢˜» ¨³ÄŸo oµ­¸¡ºÊœ 10 ˜µ¦µŠ¢»˜ Á¤Éº°…µ¥‹³Å—„o εŦ 40 µš ¤Ÿ¸ oµ¨µ¥°¥n¼ 62 ˜µ¦µŠ¢»˜ Ÿµo ¡Êœº °¥n¼ 40 ˜µ¦µŠ¢˜» ‹Š®µªµn ‡ª¦Ÿ¨˜· Á­°Êº ¨³ „µŠÁ„Š°¥µn Š¨³„˜É¸ ª´ ‹Š¹ ‹³Å—o „εŦ¤µ„šÉ­¸ —» ¨³Å—„o µÎ Ŧ­¼Š­»— ª·›š¸ ε Ÿ¨·˜Á­°ºÊ x ˜´ª Ÿ¨·˜„µŠÁ„Š y ˜ª´ ¦µ¥„µ¦ ‹Îµœªœš¸ŸÉ ¨˜· Ÿoµ¡Êºœ Ÿoµ¨µ¥ „µÎ Ŧ˜´ª¨³/µš Á­Êº° „µŠÁ„Š ‹µÎ œªœš¤¸É ¸ ­¤„µ¦‹—» ž¦³­Š‡r ………………………………………………………………………………………….. °­¤„µ¦…o°‹µÎ „—´ ‹—» ¤¤» šÅɸ —‹o µ„„¦µ¢…°Š°­¤„µ¦…°o ‹µÎ „´—‡°º ................................................................................................. ……………..................................................................................................................................................... šœ‡µn …°Š‹»—¤»¤…µo Š˜œo Ĝ­¤„µ¦‹»—ž¦³­Š‡r ‹³Å—o‡µn P —Š´ œÊ¸ ‹—» ¤»¤ š (x , y) ­¤„µ¦‹—» ž¦³­Š‡r —Š´ œ´Êœ ..............................................................................................................................................................

14 ⌫ ⌫  ⌦  ⌫      ˜ª´ °¥nµŠ ¡°n ‡µo ‡œ®œ¹ÉŠ¤„¸ µÂ¢Á„¦— A 60 „·Ã¨„¦¤´ „µÂ¢Á„¦— B 50 „·Ã¨„¦´¤ ¨³„µÂ¢Á„¦— C 60 „·Ã¨„¦¤´ Á…µ¦¦‹„» µÂ¢Ÿ­¤ 2 œ·— ×¥Ÿ­¤Á„¦— A,B ¨³ C —ªo ¥°˜´ ¦µ­nªœ 2:2:5 ¨³ 6:2:1 ˜µ¤¨Îµ—´ „µÂ¢Ÿ­¤œ—· ¦„Ä®o„εŦ „÷ ¨„¦´¤¨³ 30 µš ¨³„µÂ¢Ÿ­¤œ·—®¨Š´ Ä®o„µÎ Ŧ„·Ã¨„¦¤´ ¨³ 50 µš ‹Š®µªnµÁ…µ‹³˜o°ŠŸ­¤ „µÂ¢šŠ´Ê ­°Šœ—· °¥nµŠ¨³„É„¸ ÷ ¨„¦´¤ ‹¹Š‹³šÎµÄ®oŗo„εŦ¤µ„š­É¸ —» ª›· ¸šÎµ ¦µ¥„µ¦ ‹Îµœªœ Á„¦— A Á„¦— B Á„¦— C „εŦ„÷ ¨„¦¤´ ¨³ œ—· šÉ¸ 1 œ·—šÉ¸ 2 „µÂ¢š¸É¤¸ ­¤„µ¦‹—» ž¦³­Š‡r ………………………………………………………………………………………….. °­¤„µ¦…°o ‹µÎ „´— ‹—» ¤¤» šÉ¸Å—‹o µ„„¦µ¢…°Š°­¤„µ¦…°o ‹µÎ „´—‡°º ................................................................................................ ……………..................................................................................................................................................... šœ‡µn …°Š‹—» ¤»¤…µo Š˜oœ Ĝ­¤„µ¦‹—» ž¦³­Š‡r ‹³Å—o‡µn P —´ŠœÊ¸ ‹»—¤¤» š (x , y) ­¤„µ¦‹—» ž¦³­Š‡r —´Šœœ´Ê ..............................................................................................................................................................

⌦ 15 ⌦  „f ¡·Á«¬šoµ¥É´ªÃ¤Š 1. œ„´ ª·‹¥´ š—¨°ŠŸ­¤°µ®µ¦Ä®o­œ» …´ ×¥¤…¸ o°‹µÎ „—´ ªµn Ĝ˜¨n ³ª´œÄ®°o µ®µ¦Å—Åo ¤Án „·œ 1600 „¦¤´ ¨³ ˜°o Šž¦³„°—ªo ¥Ãž¦˜œ¸ Ťnœ°o ¥„ªnµ 58 ®œªn ¥ ¨³Å…¤œ´ Ťœn °o ¥„ªµn 40 ®œªn ¥ ¤¸°µ®µ¦°¥n¼ 2 œ·— œ—· A ˜¨n ³™»Š¦¦‹» 100 „¦´¤ ‹³¤Ã¸ ž¦˜œ¸ 3 ®œnª¥ Ņ¤´œ 4 ®œªn ¥ ¦µ‡µ 4 µš œ—· B ˜n¨³ ™»Š¦¦‹» 100 „¦´¤ ‹³¤¸Ãž¦˜¸œ 5 ®œªn ¥ Ņ¤œ´ 2 ®œªn ¥ ¦µ‡µ 5 µš ‹Š®µªµn ‹³Ä®o°µ®µ¦œ·—Ä— ‹ÎµœªœÁšµn ėŸ­¤„´œ ‹¹Š‹³Å—›o µ˜»°µ®µ¦˜µ¤˜o°Š„µ¦ ¨³¤¸¦µ‡µ™„¼ š­É¸ »— ª›· ¸šÎµ ¦µ¥„µ¦ ­¤„µ¦‹»—ž¦³­Š‡r ………………………………………………………………………………………….. °­¤„µ¦…°o ‹Îµ„´— ‹»—¤¤» šÉŸ —‹o µ„„¦µ¢…°Š°­¤„µ¦…°o ‹µÎ „´—‡°º ................................................................................................. ……………..................................................................................................................................................... šœ‡µn …°Š‹»—¤»¤…µo Š˜oœ Ĝ­¤„µ¦‹—» ž¦³­Š‡r ‹³Å—o‡µn P —´Šœ¸Ê ‹»—¤»¤ š (x , y) ­¤„µ¦‹—» ž¦³­Š‡r —Š´ œœ´Ê ..............................................................................................................................................................

16 ⌫ ⌫  ⌦  ⌫      2. 把µœŸ¨·˜¦™¥œ˜¤r ø ¦ŠŠµœŸ¨·˜ 2 ®Šn ®Šn šÉ¸ 1 Ÿ¨˜· ŗo 100 ‡œ´ ˜°n Á—°º œ ®nŠš¸É 2 Ÿ¨·˜ ŗo 110 ‡´œ ˜n°Á—°º œ ‹³˜°o Š­nŠ¦™¥œ˜År ž¥´ŠÁ¤º°Š 2 Á¤°º Š šµŠ£µ‡Á®œ°º ¨³£µ‡°¸­µœ ‡nµ…œ­Šn Áž}œ—´Š˜µ¦µŠ…µo Š¨µn Š ‹µ„ 把µœ ™¹Š £µ‡Á®œ°º ®Šn šÉ¸ 1 ®nŠš¸É 2 £µ‡°¸­µœ 100 120 60 70 ™µo Ĝ˜¨n ³Á—°º œ£µ‡Á®œº°˜°o Š„µ¦¦™¥œ˜r 80 ‡´œ ¨³£µ‡°¸­µœ˜o°Š„µ¦ 70 ‡œ´ ‹Š®µªµn ‹³‹—´ ­nŠ¦™¥œ˜r ‹µ„®nŠÄ—Åž¥Š´ £µ‡Ä—„¸‡É ´œ‹Š¹ ‹³šÎµÄ®o‡µn …œ­Šn ˜µÉÎ ­—» ª›· ¸šµÎ ¦µ¥„µ¦ ­¤„µ¦‹»—ž¦³­Š‡r ………………………………………………………………………………………….. °­¤„µ¦…°o ‹µÎ „—´ ‹»—¤»¤šÉŸ —‹o µ„„¦µ¢…°Š°­¤„µ¦…°o ‹µÎ „´—‡º° ................................................................................................. ……………..................................................................................................................................................... šœ‡µn …°Š‹—» ¤»¤…µo Š˜œo Ĝ­¤„µ¦‹—» ž¦³­Š‡r ‹³Å—‡o µn P —´ŠœÊ¸ ‹—» ¤»¤ š (x , y) ­¤„µ¦‹»—ž¦³­Š‡r —´ŠœÊ´œ ..............................................................................................................................................................

⌦ 17 ⌦ 3. ­Îµœ„´ ŠµœÂ®nŠ®œ¹ÉŠ˜°o Š„µ¦Žº°Ê ˜Áo¼ „È Á°„­µ¦ 2 œ—· ‡º°œ—· A „´œ·— B ×¥šÉ¸ œ—· A ĝ¨³ 1,000 µš œ·— B ĝ¨³ 2,000 µš œ—· A ¤¸‡ªµ¤‹» 8 ¢˜» 3 ˜°o ŠÄo¡ºÊœšÉ¸Äœ„µ¦‹—´ ªµŠ 6 ¢˜» 2 œ·— B ¤‡¸ ªµ¤‹» 12 ¢»˜3 ˜o°ŠÄo¡œºÊ šÉĸ œ„µ¦‹—´ ªµŠ 8 ¢˜» 2 ™µo ¤¸Šž¦³¤µ–ŤÁn „œ· 14,000 µš ¨³ ¤¸¡ºœÊ šÉ¸Äœ„µ¦‹´—ªµŠ 72 ¢˜» 2 ‹Š®µªµn ‹³˜o°ŠŽ°ºÊ ˜¼oÁ„È Á°„­µ¦œ—· ¨³„˜É¸ ‹o¼ ¹Š‹³Á„È Á°„­µ¦Å—¤o µ„š¸É­»— ª›· ¸šµÎ ¦µ¥„µ¦ ­¤„µ¦‹—» ž¦³­Š‡r ………………………………………………………………………………………….. °­¤„µ¦…°o ‹µÎ „´— ‹—» ¤»¤šÉ¸Å—‹o µ„„¦µ¢…°Š°­¤„µ¦…o°‹Îµ„´—‡º° ................................................................................................. ……………..................................................................................................................................................... ……………..................................................................................................................................................... šœ‡µn …°Š‹»—¤»¤…oµŠ˜oœ Ĝ­¤„µ¦‹»—ž¦³­Š‡r ‹³Å—‡o nµ P —´ŠœÊ¸ ‹—» ¤¤» š (x , y) ­¤„µ¦‹»—ž¦³­Š‡r —´ŠœÊœ´ ..............................................................................................................................................................

18 ⌫ ⌫  ⌦  ⌫      4. 把µœŸ¨·˜…°ŠÁ¨nœÂ®nŠ®œÉŠ¹ Ÿ¨·˜˜»p„˜µÂ¨³¦™Á—„È Á¨œn ×¥˜„»p ˜µ‹³…µ¥Å—o„µÎ ŦÊœ· ¨³ 10 µš ¦™Á—È„ Á¨œn ‹³…µ¥Å—„o µÎ ŦœÊ· ¨³ 12 µš Ĝ„µ¦Ÿ¨·˜…°Šš´ŠÊ ­°Š°¥nµŠ˜o°ŠŸnµœÁ‡¦É°º Š°´—Â¨³Á‡¦°Éº Š¡œn ­¸ ×¥šÉ¸ ˜„»p ˜µÄÁo ª¨µÄœ„µ¦°´— 2 œµš/¸ Ê·œ ¦™Á—„È Á¨nœ 1 œµš/¸ ·œÊ Ĝ„µ¦¡nœ­¸ ˜»p„˜µÄÁo ª¨µ 1 œµš/¸ ·Êœ ¦™Á—È„Á¨nœÄoÁª¨µ 3 œµš¸/Êœ· Ĝ˜n¨³ªœ´ Á‡¦É°º Š°´—¤¸Áª¨µªµn Š­Îµ®¦´…°ŠÁ¨nœšŠ´Ê ­°Š°¥nµŠ 6 Éª´ äŠ Á‡¦ºÉ°Š¡nœ­¸¤¸Áª¨µªnµŠ 5 ª´É äŠ ‹Š®µªnµ‹³˜°o ŠŸ¨·˜…°ŠÁ¨œn ª´œ¨³Ášµn ė‹Š¹ ‹³¤„¸ µÎ Ŧ­¼Š­»— ª›· š¸ µÎ ¦µ¥„µ¦ ­¤„µ¦‹—» ž¦³­Š‡r ………………………………………………………………………………………….. °­¤„µ¦…o°‹Îµ„—´ ‹»—¤¤» š¸Éŗ‹o µ„„¦µ¢…°Š°­¤„µ¦…°o ‹µÎ „´—‡°º ................................................................................................. ……………..................................................................................................................................................... ……………..................................................................................................................................................... ……………..................................................................................................................................................... šœ‡nµ…°Š‹»—¤¤» …µo Š˜oœ Ĝ­¤„µ¦‹—» ž¦³­Š‡r ‹³Å—o‡nµ P —´Šœ¸Ê ‹»—¤»¤ š (x , y) ­¤„µ¦‹»—ž¦³­Š‡r —Š´ œœÊ´ ...............................................................................................................................................................

⌦ 19 ⌦ 5. «¦­¸ —» µ¤œ¸ ÎµÊ ˜µ¨ 6000 „¦¤´ ¨³ÂžjŠ 16,000 „¦¤´ ­µÎ ®¦´ šÎµ…œ¤ 2 œ·— ‡º° A ¨³ B ×¥šÉ¸ œ—· A ˜n¨³œÊ· ˜°o ŠÄoœÎµÊ ˜µ¨ 100 „¦¤´ ¨³ÄÂo žŠj 300 „¦´¤ Á¤º°É …µ¥Åž‹³Å—o„εŦœ·Ê ¨³ 4 µš œ—· B ˜¨n ³ ·Êœ ˜o°ŠÄoœÊ嘵¨ 150 „¦¤´ ¨³ÄožŠj 250 „¦´¤ Á¤°ºÉ …µ¥Åž‹³Å—„o µÎ Ŧ·œÊ ¨³ 5 µš „ε®œ— P šœ „εŦ‹µ„„µ¦…µ¥ x šœ‹Îµœªœ…œ¤œ·— A y šœ‹Îµœªœ…œ¤œ·— B 3.1. ‹Š®µ­¤„µ¦‹—» ž¦³­Š‡rĜ„µ¦‡µÎ œª–ªnµ«¦¸­»—µ‡ª¦šÎµ…œ¤œ—· ¨³„¸Éœ·Ê ‹Š¹ ‹³Å—o„µÎ Ŧ­Š¼ ­»— „. P = 4x + 5y …. P = 5x + 4y ‡. P = 100x + 150y Š. P = 300x + 250y 3.2. ‹Š®µ°­¤„µ¦…o°‹µÎ „´—Á¡É·¤Á˜¤· ‹µ„ xt0 ¨³ yt0 ž¦³„°„µ¦‡Îµœª–®µªµn «¦¸­»—µ‡ª¦ šµÎ …œ¤œ·—¨³„¸É ʜ· ‹¹Š‹³Å—„o µÎ Ŧ¤µ„š­É¸ —» „. 10 x  30y d 600 …. 30 x  10y d 600 15x  25y d 1600 25x  15y d 1600 ‡. 15 x  10y d 600 Š. 10 x  15y d 600 25x  30y d 1600 30x  25y d 1600 6. ®µo Š­¦¦¡­·œ‡oµ ¤¡¸ œºÊ š¸É ´Êœ¨µn Š¦ª¤ 100,000 ˜µ¦µŠ¢»˜ Á¡ºÉ°˜Ê´Š…µ¥­œ· ‡oµ 3 œ—· ŗÂo „n 1. Á‡¦Éº°Š­Îµ°µŠ 2. Á­Êº°Ÿµo ­ÎµÁ¦È‹¦ž¼ 3. …°ŠÄ°o ºÉœÇ šÉ´ªÅž ‹µ„‡ÎµÂœ³œÎµ…°Šœ´„°°„ŽŠ¹É °„ªµn ¡ºÊœš¸É­µÎ ®¦´ Ÿœ„Á‡¦°Éº Š­Îµ°µŠÅ¤n‡ª¦˜µÎÉ „ªµn 50% …°Š¡œºÊ šÉ¸´œÊ ¨nµŠšÊŠ´ ®¤— ¨³¡Êºœš¸É¦ª¤…°ŠÂŸœ„ Á‡¦º°É Š­Îµ°µŠ„´ Ÿœ„…°ŠÄ°o œÉº Ç šªÉ´ ŞŤ‡n ª¦¤µ„„ªnµ¡Êœº š¸É…°ŠÂŸœ„Á­ºÊ°Ÿoµ­ÎµÁ¦‹È ¦ž¼ Á„œ· 3000 ˜µ¦µŠ¢»˜ ‹µ„„µ¦ž¦³¤µ–Ÿ¨„εŦ…°ŠÂŸœ„˜nµŠÇ ŗo—Š´ œ¸Ê Ÿœ„Á‡¦º°É Š­Îµ°µŠ 1,000 µš/˜µ¦µŠ¢»˜/Á—º°œ Ÿœ„Á­ºÊ°Ÿµo ­ÎµÁ¦‹È ¦¼ž 600 µš/˜µ¦µŠ¢˜» /Á—°º œ Ÿœ„…°ŠÄo°œÉº Ç šÉª´ Ş 800 µš/˜µ¦µŠ¢˜» /Á—°º œ ®oµŠ­¦¦¡­œ· ‡µo ŗo‹—´ ¡œÊº š˜É¸ µ¤‡µÎ œ³œµÎ …°Šœ„´ °°„ 4.1. ®oµŠ­¦¦¡­·œ‡oµ‹³Å—„o µÎ Ŧ­¼Š­»— Á¤É°º ‹—´ ¡Êœº š­É¸ µÎ ®¦´ÂŸœ„Á‡¦É°º Š­µÎ °µŠ„¸˜É µ¦µŠ¢˜» „. 50,500 ˜µ¦µŠ¢»˜ …. 51,500 ˜µ¦µŠ¢»˜ ‡. 52,500 ˜µ¦µŠ¢»˜ Š. 53,500 ˜µ¦µŠ¢˜» 4.2. ®oµŠ­¦¦¡­œ· ‡µo ‹³Å—„o εŦ­¼Š­»—„ɝ¸ µš˜n°Á—°º œ „. 80,000,000 µš …. 80,300,000 µš ‡. 80,600,000 µš Š. 80,900,000 µš

20 ⌫ ⌫  ⌦  ⌫      š¸žÉ ¦„¹ ¬µ : Ÿ—¼o εÁœ·œ„µ¦ —¦.°µÎ ¦Š» ‹œ´ šªµœ· —¦.­¦· ·¡¦ » µœ´œ˜r Á¨…µ›„· µ¦­£µ„µ¦«¹„¬µ ¦«.—¦.­Îµ°µŠ ®¦· ´¦¼ –³ ¦°ŠÁ¨…µ›„· µ¦­£µ„µ¦«„¹ ¬µ —¦.¦n»ŠÁ¦°º Š ­»…µ£·¦¤¥r …µo ¦µ„µ¦Îµœµ š¸Éž¦„¹ ¬µÃ‡¦Š„µ¦² œµŠ­µª­»š›µ­œ· ¸ ª´¦¨¼ Ÿ˜¼o ¦ª‹¦µ„µ¦„¦³š¦ªŠ«¹„¬µ›„· µ¦ šžÉ¸ ¦„¹ ¬µÃ‡¦Š„µ¦² œµŠ­µª‹·¦¡¦¦– ž»–Á„¬¤ šž¸É ¦¹„¬µ—oµœ¦³„µ¦«¹„¬µ ­„«. Ÿo¼°Îµœª¥„µ¦­µÎ œ´„¤µ˜¦“µœ„µ¦«¹„¬µÂ¨³¡´•œµ„µ¦Á¦¥¸ œ¦o¼ Ÿo¼Á¦¥¸ Á¦¥¸ Š : æŠÁ¦¥¸ œ¤®µª·¦µª›» ‹´Š®ª—´ ­Š…¨µ œµŠ‹¦» ¸ Á¦°º ŠÁ¦Š· „»¨§š›·Í Ÿ¼˜o ¦ª‹šµœ : ¦°Š«µ­˜¦µ‹µ¦¥°r µ¦·­µ ¦´˜œÁ¡È¦r ®´ª®œµo ‡–³ª‹· ´¥ —¦.«»£ª¦¦– Á¨·«Å„¦ °µ‹µ¦¥Ár °›´­ª•´ œr ‡µÎ ¤–¸ °µ‹µ¦¥­r ›» ˜· µ ¤–¸ ¥´ ‡–³°µ‹µ¦¥rŸo¼­°œ‡–˜· «µ­˜¦Ãr ¦ŠÁ¦¸¥œš¸ÁÉ …oµ¦nª¤Ã‡¦Š„µ¦² ‹µ„æŠÁ¦¸¥œ—´Š˜n°ÅžœÊ¸ x æŠÁ¦¸¥œ®µ—Ä®ªn ·š¥µ¨¥´ ‹Š´ ®ª´—­Š…¨µ x æŠÁ¦¸¥œ¤®µª·¦µª›» ‹´Š®ª´—­Š…¨µ x æŠÁ¦¸¥œ¦¼ –³¦µÎ ¨¹„ ‹´Š®ª—´ ˜¦´Š x æŠÁ¦¥¸ œ‹¯» µ£¦–¦µªš· ¥µ¨´¥ ‹´Š®ª—´ ­˜¼¨ x æŠÁ¦¥¸ œ­¦» µ¬’¦r›µœ¸ ‹Š´ ®ª´—­¦» µ¬’¦r›µœ¸ x æŠÁ¦¥¸ œ¡»œ¡œ· ¡š· ¥µ‡¤ ‹Š´ ®ª´—­¦» µ¬’¦r›µœ¸ x æŠÁ¦¥¸ œÁ˜¦¥¸ ¤°»—¤£µ‡Ä˜o ‹Š´ ®ª´—œ‡¦«¦›¸ ¦¦¤¦µ Ÿ¡¼o ·‹µ¦–µ¦µ¥Šµœ : œµŠ­µª­œ» œ´ šµ œ¨· ­·š›­·Í ™µ¡¦ æŠÁ¦¸¥œÁ˜¦¥¸ ¤°—» ¤«„¹ ¬µ „¦Š» Áš¡² Ÿ¦o¼ ´ Ÿ·—°Ã‡¦Š„µ¦ : ®´ª®œoµÃ‡¦Š„µ¦ œµŠ­µª»Áš¸¥¤ «·¦·ž{µ ž¦³‹µÎ ǦŠ„µ¦ œµ¥¦ª· ˜µÂ„oª ž¦³‹µÎ ǦŠ„µ¦ œµŠ­µª„ŠÉ· „µ‹œr Á¤‰µ ž¦³‹ÎµÃ‡¦Š„µ¦ œµ¥«·¦¦· ˜´ œr Îµœµ„·‹ ¦¦–µ›·„µ¦ : œµŠ­µª»Áš¸¥¤ «¦· ·ž{µ œµŠ­µª„·ÉŠ„µ‹œr Á¤‰µ Á¦¥¸ Á¦¥¸ ŠÂ¨³‹—´ šÎµ¦µ¥Šµœ : œµŠ­µª„ÉŠ· „µ‹œr Á¤‰µ

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