Problem 1   (TAY 44-45/161adjusted)                         The Metro Food Services Company delivers fresh sandwiches eachmorning to vending machines throughout the city. The company makesthree kinds of sandwiches – ham and cheese, bologna, and chickensalad. A ham and cheese sandwich requires a worker 0.90 minutes toassemble, a bologna sandwich requires a worker 0.80 minutes, and achicken salad sandwich requires a worker 1.00 minutes to make. Thecompany has 6 workers available each night to assemble sandwiches(i.e. 2,880 minutes). Vending machine capacity is available for3,000 sandwiches each day. The profit for a ham and cheese sandwichis 70¢ (i.e. $0.70), the profit for a bologna sandwich is 85¢, andthe profit for a chicken salad sandwich is 75¢. The company knowsfrom past sales records that their customers buy as many or more ofthe ham and cheese sandwiches than the other two sandwichescombined. But customers need a variety of sandwiches available, soMetro stocks at least 300 of each sandwich type. Metro managementwants to know how many of each sandwich it should stock to maximizeprofit.

Formulate this decision question as a Linear Programming Model.Define the variables, write down the constraints and the objectivefunction in mathematical (algebraic) terms (variables,inequalities, etc.).

Find the optimal solution using SOLVER.

Answer as many parts below as possible withoutre-running Solver. (do each part independently from the others) Usethe SENSITIVITY REPORT whenever possible.

If Metro Food Services could hire another worker and increaseits available assembly time by 480 minutes, or increase its vendingmachine capacity by 200 sandwiches, which should it do? How muchadditional profit would your decision result in?

What would the effect be on the optimal solution if the profitfor a ham and cheese sandwich were increased to 80¢?   to90¢?