Case Problem: Restaurant du Pares

Chloe Montenegro and Angeli Dimagiba are close friends since childhood. Upon graduation, Chloe and Angeli thought of setting up a joint business venture. The two friends decided to open a restaurant near the State University where they studied food and nutrition. Inspired by the charm and romance of the City of Light, they named the restaurant "Restaurant du Pares."

Chloe and Angeli knew in advance that at least initially they could not offer a full, varied menu of dishes. They decided to serve only two main courses, a braised beef stew dish and the other a fish fillet dish. Their chief cook, Petr, was confident he could make each dish so exciting and unique that two meals would be sufficient, at least until they could assess which menu items were most popular. Petr indicated that with each meal he could experiment with different appetizers, soups, salads, vegetable dishes, and desserts until they were able to identify a full selection of menu items.

The next problem for Chloe and Angeli was to determine how many meals to prepare for each day so they could shop for ingredients and set up the work schedule. They could not afford too much waste. Their supply of beef is limited to making $300$ meals each day. They estimated that they would sell a maximum of $600$ dishes each day. Each beef dinner, including all accompaniments, requires $30$ minutes to prepare, while each fish dinner takes half as long. There is a total of $200$ hours of kitchen staff labor available each day.

Chloe and Angeli believe that because of the health consciousness of their potential clientele, they will sell at least three fish dinners for every two beef dinners. However, they also believe that at least $10\%$ of their customers will order beef dinners. The profit from each beef dinner will be approximately P$160,$ and the profit from a fish dinner will be about P$120.$

a$.$ Formulate a linear programming model for Chloe and Angeli that will help them estimate the number of meals they should prepare each day.

b$.$ How many units of each meal should they prepare each day and what will be the daily profit?

c$.$ What constraints are limiting profit?

Before they make the final meal preparation plan, Chloe and Angeli plan to explore the following questions independently, except where otherwise indicated.

d$.$ Should Chloe and Angeli cednsider looking for additional suppliers of beef? Explain your answer.

e$.$ Suppose they reconsidered the demand for beef dinners and decided that at least $20\%$ of their customers would purchase beef dinners. What effect would this have on their meal preparation plan?

f$.$ If Chloe and Angeli increased the menu price on the fish dinner so that the profit for both dinners was the same, what effect would that have on their solution?

PLEASE SOLVE IN EXCEL