The Burger Place is a local shop that plans to make its sales this Saturday from its sidewalk tables during the town's holiday parade. On this occasion, the shop's owners know that customers will buy the burger and any burger offered will sell completely. The Burger Place offers plain, cheese, bacon, and deluxe burgers. Each variety has its own requirement of patties, cheese, buns, and toppings (in ounces per pizza as shown in the table), and each has its own selling price (per pizza).

Plain Cheese Bacon Deluxe Available

Buns 5 5 5 5 200

Patties 3 3 3 3 90

Cheese 4 3 3 4 120

Bacon 0 3 0 2 75

Toppings 0 0 3 2 40

Price $6 $8 $10 $12

The Burger Place would like to determine what is the right combination of burgers to make (using its existing stock of ingredients) to maximize revenue from its sales. [Please note that in LP problems one does not use integer constraints.]

a)Write the Linear Program formulation for the above optimization problem. Make your formulation clear by defining the variables, constraints, objective function etc. clearly.

b)Solve it using Excel solver. Please attach your clearly annotated Solver model and output (including Answer and Sensitivity Report) as Exhibit A.

c)What is the maximum sales revenue? What mix of burgers should be made to achieve this sales revenue?

d)Which ingredients are economically scarce (i.e., they are limiting to profits)?

The following questions can be answered using the sensitivity report (the more tedious way to answer the question is by running Solver after changing the data, by trial and error).

e)Plain and Deluxe pizzas are not being produced in the optimal production plan. By how much should their selling price go up to make it economically sensible to produce plain and vegetable pizzas?

f) The availability of sauce has gone down by 10 units. What will the new sales revenue be?