In this case study you will develop a linear programming model for determining the optimal

production schedule which minimizes total cost of production. An important part of this case

study is to develop the layout, formatting, and structure of the model so that it meets the

spreadsheet engineering requirements we discussed in class.

a$)$ Develop a linear programming model for this problem. Your model should include

calculation of unit costs of producing the three products in$-$house.

b$)$ In a MS Word document write a brief explaining the following:

$$ The production schedule that minimizes total cost.

$$ Which labor and material resources completely used up$,$ and what are the

corresponding shadow prices?

$$ What is the production schedule if hand cream can be subcontracted out at a cost

of $$50$ per carton?

$$ What is the production schedule if the demand for each product is increased by

$10\%,$ assuming that hand cream can be outsourced at $$50$ per carton. Note: The

spreadsheet model should be designed to work if this percentage is changed.