A fertilizer manufacturer has to fulfill supply contracts to its two main customers (650 tons to Customer A and 800 tons to Customer B). It can meet this demand by shipping existing inventory from any of its three warehouses. Warehouse 1 (W1) has 400 tons of inventory on hand, Warehouse 2(W2) has 500 tons, and Warehouse 3 (W3) has 600 tons. The company would like to arrange the shipping for the lowest cost possible, where the per-ton transit costs are as follows:

(a) Explain what each of the six decision variables (V) is:

V A1: ________________________________________

V A2: ________________________________________

V A3: ________________________________________

V B1: ________________________________________

V B2: ________________________________________

V B3: ________________________________________

(b) Write out the objective function in terms of the variables (V A₁, V A₂, etc.) and the objective coefficients.

(c) Aside from nonnegativity of the variables, what are the five constraints? Write a short description for each constraint, and write out the formula (and circle the type of equality/inequality).

After you formulate and enter the linear program for Problem B.27 in Excel, the Solver given you the following sensitivity report:

(d) How many of the constraints are binding?

(e) How much slack/surplus is there with the nonbinding constraint(s)

(f) What is the range of optimality on variable V A3?

(g) If we could shop 10 tons less to Customer a, how much money might we be able to save? If we could chose to short either Customer A or Customer B by 10 tons, which would we prefer to short? Why?

Transcribed Image Text:

W3 W2 $6.25 W1 Customer A Customer B $6.50 8.00 $7.50 6.75 7.00 ne