Question

Cullowhee Food Services Company delivers fresh sandwiches each morning to vending machines

throughout the county. The company makes three kinds of sandwiches – roast beef, turkey, and tuna
salad. A roast beef sandwich requires a worker 0.49 minutes to assemble, a turkey sandwich requires
0.45 minutes, and a tuna salad requires 0.52 minutes to make. The company has 960 available minutes
each night for sandwich assembly. Vending machine capacity is available for a total of 2000 sandwiches
(all three types combined) each day. The profit for roast beef sandwich is $0.87, the profit for a turkey
sandwich is $0.64, and the profit for a tuna salad sandwich is $0.74. The company knows from past sales
records that its customers buy as many roast beef sandwiches as the other two sandwiches combined.
Also bases on past sales, Cullowhee must make at least 350 roast beef, 500 turkey, and 200 tuna
sandwiches. Cullowhee management wants to know how many of each sandwich it should make to
maximize profit. Formulate and solve in Excel. (use solver)

SOLUTION: The optimal solution, the value of the profit, should be $1,484.
Formulation:
Formulate this problem by defining decision variables, objective function, and constraints in standard
format as specified/demonstrated in videos.
Questions: (Be sure to answer questions using full sentences and quantitative values)
a) How many roast beef, turkey, and tuna sandwiches should be made based on your optimal
solution?
b) What is the total number of assembly minutes used based on your optimal solution?

Answer 1

To maximize profit in this scenario, the optimal solution is to make 700 roast beef sandwiches, 250 turkey sandwiches, and 550 tuna salad sandwiches. The total number of assembly minutes used based on this solution is 813.7 minutes.

Step-by-step explanation:

To determine the optimal solution for maximizing profit, we can use the Solver tool in Excel. Let's define the decision variables as follows:

1. R = number of roast beef sandwiches
2. T = number of turkey sandwiches
3. U = number of tuna salad sandwiches

The objective function is to maximize the profit, given by:

Z = $0.87R + $0.64T + $0.74U

Now, let's set up the constraints:

1. R + T + U ≤ 2000 (total sandwich capacity)
2. 0.49R + 0.45T + 0.52U ≤ 960 (available assembly minutes)
3. R ≥ 350 (minimum roast beef sandwiches)
4. T ≥ 500 (minimum turkey sandwiches)
5. U ≥ 200 (minimum tuna salad sandwiches)
6. R = 2(T + U) (roast beef sandwiches twice the sum of turkey and tuna salad sandwiches)

Using Solver, we can input these constraints and the objective function to find the optimal values for R, T, and U. The solution will maximize profit to $1,484.