Formulate the Following as a Linear Programming Problem

question 114

Essay

Formulate the following as a linear programming problem.
Jan lives in the country and is having a garage sale tomorrow. She has decided to sell some fresh baked goods in conjunction with the sale. She has excellent recipes for apple pie and for apple turnovers. She has 20.83 pounds of apples. Each pie will require 1.6 pounds of apples and each turnover will require 0.22 pounds of apples. She has discovered that she is short of both flour and sugar and does not want to make another trip to the store tonight. She has 5.7 pounds of flour and 200 grams of sugar. Each pie will require 0.6 pounds of flour and 11 grams of sugar. Each turnover will require .02 pounds of flour and 3 grams of sugar. She will sell pies for $6 each and turnovers for $0.75 each. She has decided to make 8 pies at most, because she is concerned about how well they will sell.

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Definitions:

Direct Hours

Hours worked directly on a specific task or product, often used in calculating labor costs in manufacturing.

Direct Materials

Raw materials that can be directly attributed to the production of a specific product or service.

Selling Price

The amount of money a customer pays to purchase a product or service.

Predetermined Overhead Rate

A rate used to allocate manufacturing overhead costs to products based on a set criteria, like direct labor hours.