The Waygate Corporation makes five different types of metal casing for personal computers. The company is in the process of replacing its machinery with three different new models of metal stamping machines: the Robo-I, Robo-II, and Robo-III. The unit costs of each machine are $18,500, $25,000, and $35,000, respectively. Each machine can be programmed to produce any of the five casings. Once the machine is programmed, it produces each type of casing at the following rates:

The company has the following goals:
Goal 1: To spend no more than approximately $400,000 on the purchase of new machines
Goal 2: To have the ability to produce approximately 3,200 units of type 1 casings per hour
Goal 3: To have the ability to produce approximately 2,500 units of type 2 casings per hour
Goal 4: To have the ability to produce approximately 3,500 units of type 3 casings per hour
Goal 5: To have the ability to produce approximately 3,000 units of type 4 casings per hour
Goal 6: To have the ability to produce approximately 2,500 units of type 5 casings per hour
a. Formulate a GP model for this problem. Assume that all percentage deviations from all goals are equally undesirable.
b. Implement your model in a spreadsheet and solve it.
c. What is the optimal solution?
d. What is the solution that minimizes the maximum percentage deviation from all the goals?
e. Assume that the company can spend no more than $400,000. What is the solution that minimizes the maximum percentage deviation from all the remaininggoals?

Casings per Hour TypeType 2 Type 3 Type 210 220 180 Type 5 Robo-I Robo-II Robo-III 200 100 265 130 235 160 140 170 260 80 120 220