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 $$35,000,$ respectively. Each machine can be programmed to produce any of the five casings. After the machine is programmed it produces each type of casing at the following rates: Casings per Hour Type $1$Type $2$Type $3$Type $4$Type $5$Robo$-$I$10012014020080$Robo$-$II$260230170220120$Robo$-$III$200160260180220$ Goal $1$: To spend no more than approximately $$400,000$ on the purchase of new machinesGoal $2$: To have the ability to produce approximately $3,200$ units of type $1$ casings per hourGoal $3$: To have the ability to produce approximately $2,500$ units of type $2$ casings per hourGoal $4$: To have the ability to produce approximately $3,500$ units of type $3$ casings per hourGoal $5$: To have the ability to produce approximately $3,000$ units of type $4$ casings per hourGoal $6$: To have the ability to produce approximately $2,500$ units of type $5$ casings per houra. 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?