: A small chip manufacturer sells three types of chips. The maximum demand for chips type A$,$ B$,$ and C can be $150,100,$ and $30$ per day respectively. ABC has a daily machine capacity of $1200$ hours, with each model A$,$ B$,$ and C taking $5,8$ and $12$ machine hours respectively to produce. The chip types A$,$ B$,$ and C use $8,10,$ and $12$ semiconductors respectively. The manufacturer can get a supply of maximum $2000$ semiconductors each day. Chip type A$,$ B$,$ and C yields a profit of $$20,$ $$30$ and $70$ respectively.

ABC has the following goals for the company $(1).$ Maximize profit, $(2).$ Maximize number of chips produced.

a$)$ Formulate this Goal programming problem. $($Note that units produced are integer

Let

b$)$ Solve the LP problems to maximize each goal. Show both solutions and objective functions.

c$)$ Solve the goal programming problem to minimize the maximum $\%$ deviation from each goal. Show the target for each goal, the $\%$ deviation from each goal, and your solution.

d$)$ What will be new solution if Goal # $1$ was twice as important as Goal # $2?$