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A small company produces two types of margarine: type A (Lowfat) and type B (Verylowfat). The production costs are €0.7 per kg for type A and €0.8 per kg for type B: The daily demands 94 of type A and qe of type B are given by 4A = 160-200PA+100PB and qB = 60+100PA - 100qB where PÅ and PB represent the prices (in € per kg) for the two types of margarine. It is known that the daily demand of type B is 25 kg. a. Determine the profit function P that gives the total profit for the two types of margarine in terms of PA b. What selling prices give the maximum profit? Use derivatives to solve this question. c. Determine the maximum profit.

A small company produces two types of margarine: type A (Lowfat) and type B (Verylowfat). The production costs are €0.7 per kg for type A and €0.8 per kg for type B: The daily demands 94 of type A and qe of type B are given by 4A = 160-200PA+100PB and qB = 60+100PA - 100qB where PÅ and PB represent the prices (in € per kg) for the two types of margarine. It is known that the daily demand of type B is 25 kg. a. Determine the profit function P that gives the total profit for the two types of margarine in terms of PA b. What selling prices give the maximum profit? Use derivatives to solve this question. c. Determine the maximum profit.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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9. A small company produces two types of margarine: type A (Lowfat) and type B (Verylowfat). The production costs are €0.7 per kg for type A and €0.8 per kg for type B: The daily demands 44 of type A and qe of type B are given by 9A= 160-200PA+ 100PB and qB = 60+ 100PA - 100qB where PÅ and PB represent the prices (in € per kg) for the two types of margarine. It is known that the daily demand of type B is 25 kg. a. Determine the profit function P that gives the total profit for the two types of margarine in terms of PA- b. What selling prices give the maximum profit? Use derivatives to solve this question. c. Determine the maximum profit.
Transcribed Image Text:9. A small company produces two types of margarine: type A (Lowfat) and type B (Verylowfat). The production costs are €0.7 per kg for type A and €0.8 per kg for type B: The daily demands 44 of type A and qe of type B are given by 9A= 160-200PA+ 100PB and qB = 60+ 100PA - 100qB where PÅ and PB represent the prices (in € per kg) for the two types of margarine. It is known that the daily demand of type B is 25 kg. a. Determine the profit function P that gives the total profit for the two types of margarine in terms of PA- b. What selling prices give the maximum profit? Use derivatives to solve this question. c. Determine the maximum profit.
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