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A baker wants to bake two kinds of cookies, which both need raisins and walnuts as ingredients. A dozen of the first kind need 3 ounces of walnuts and 3 ounces of raisins, while a dozen of the second kind requires 2 ounces of walnuts and 5 ounces of raisins. Since the baker has not yet replenished his stock of ingredients he found out that he has only 2 lbs. of walnuts, and 3 lbs and 5 ounces of raisins left (note: 1 pound = 16 ounces). a) If he wants to maximize his profit, how many dozens of each kind should he bake if his profit for a dozen of the first kind is P48 and for the second kind is P60? b) What would happen to the baker's profit if he had 2.5 lbs of walnuts available instead of 2 lbs? c) What would happen to the baker's profit if he found out his son ate some of his raisin stock and that he only have 2 lbs and 10 ounces of raisins left? d) What would the range of weight of walnuts available that would make its current dual price still valid? Only Sub part D is required to be solved on this question

A baker wants to bake two kinds of cookies, which both need raisins and walnuts as ingredients. A dozen of the first kind need 3 ounces of walnuts and 3 ounces of raisins, while a dozen of the second kind requires 2 ounces of walnuts and 5 ounces of raisins. Since the baker has not yet replenished his stock of ingredients he found out that he has only 2 lbs. of walnuts, and 3 lbs and 5 ounces of raisins left (note: 1 pound = 16 ounces). a) If he wants to maximize his profit, how many dozens of each kind should he bake if his profit for a dozen of the first kind is P48 and for the second kind is P60? b) What would happen to the baker's profit if he had 2.5 lbs of walnuts available instead of 2 lbs? c) What would happen to the baker's profit if he found out his son ate some of his raisin stock and that he only have 2 lbs and 10 ounces of raisins left? d) What would the range of weight of walnuts available that would make its current dual price still valid? Only Sub part D is required to be solved on this question

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 107P
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A baker wants to bake two kinds of cookies, which both need raisins and walnuts as ingredients. A dozen of the first kind need 3 ounces of walnuts and 3 ounces of raisins, while a dozen of the second kind requires 2 ounces of walnuts and 5 ounces of raisins. Since the baker has not yet replenished his stock of ingredients he found out that he has only 2 lbs. of walnuts, and 3 lbs and 5 ounces of raisins left (note: 1 pound = 16 ounces).

a) If he wants to maximize his profit, how many dozens of each kind should he bake if his profit for a dozen of the first kind is P48 and for the second kind is P60?

b) What would happen to the baker's profit if he had 2.5 lbs of walnuts available instead of 2 lbs?

c) What would happen to the baker's profit if he found out his son ate some of his raisin stock and that he only have 2 lbs and 10 ounces of raisins left?

d) What would the range of weight of walnuts available that would make its current dual price still valid?

Only Sub part D is required to be solved on this question

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