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 dif$-$

ferent 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. After 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 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 remaining goals?