Question: Transportation problem (20 pts)

Trisha Mellon, the owner of Waltzer Catering Service, is booked to cater a banquet every evening for the next 4 days. She requires clean napkins every day, as follows: 100 for day 1, 130 for day 2, 150 for day 3, and 140 for day 4. She may send dirty napkins to the laundry, which has two types of service – overnight and regular. The overnight service will have napkins ready for the banquet the following day; the regular service will have napkins ready in two days. The overnight service costs $6 per item and the regular service cost $4 per item. Ms Mellon may also choose to purchase new napkins at any time at a cost of $10 per item. She has an initial stock of 200 napkins. She wants to minimize the total cost of supplying fresh napkins for the next 4 days.

a. Draw the network diagram of this problem, by showing the nodes, arcs and costs.

b. Formulate the LP problem algebraically, by defining the decision variables, the objective function and the constraints.

c. Using Solver, find the optimal solution and the total cost.