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## Homework Statement

**Linear Programming Case Study - Case Problem ( Page # 109 Decision making methods) “The Possibility” Restaurant?**

In the case problem, Angela and Zooey wanted to develop a linear programming model to help determine the number of beef and fish meals they should prepare each night. Solve Zooey and Angela’s linear programming model by using QM.

Angela and Zooey are considering investing in some advertising to increase the maximum number of meals they serve. They estimate that if they spend $30 per day on a newspaper ad, it will increase the maximum number of meals they serve per day from 60 to 70. Should they make the investment?

Zooey and Angela are concerned about the reliability of some of their kitchen staff. They estimate that on some evenings they could have a staff reduction of as much as 5 hours. How would this affect their profit level?

The final question they would like to explore is raising the price of the fish dinner. Angela believes the price for a fish dinner is a little low and that it could be closer to the price of a beef dinner without affecting customer demand. However, Zooey has noted that Pierre has already made plans based on the number of dinners recommended by the linear programming solution. Angela has suggested a price increase that will increase profit for the fish dinner to $14. Would this be acceptable to Pierre, and how much additional profit would be realizes?

## Homework Equations

can someone please help me solve this? I need something like this:

Resource Availability 1200 minutes of labor per day

60 maximum meals each night

Decision variables

X1 = number of fish meal

X2 = number of beef meal

Objective function Maximize

Z = $12X1 + $16X2

Where Z = total profit per day

$12X1 = profit from fish meals

$16X2 = profit from beef meals

Resource Constraints

X1 + X2 ≤ 60 (the maximum estimated meals each night)

15X1 + 30X2 ≤ 1200 (labor in minutes to prepare meals)

2X1 - 3X2 ≥ 0 (they'll sell at least 3fish/2beef meal)

X1 - 9X2 ≤ 0 (at least10% of customers will order beef meal)

Non-Negativity Constrains

X1 ≥ 0 ; X2 ≥ 0