$(15$ points$)$ Formulate the linear programming problem A technology company

makes quarterly decision about two products: laptop computers and desktop comput$-$

ers. Each computer $($laptop and desktop$)$ requires a Processing Chip. Each computer

also requires a Memory Chip. Memory comes in $64$ MB chip sets. A laptop computer

has $64$ MB memory installed $($so needs $1$ memory chip set$)$ while a desktop computer

has $128$ MB $($so needs $2$ memory chip sets$).$ The company has $10,000$ processing chips

and $15,000$ memory chips available. Each computer requires assembly time. A laptop

computer takes more time to assemble: $4$ minutes versus $3$ minutes for a desktop. There

are $420$ hours of assembly time available in the next quarter. Given current market

conditions, material cost, and our production system, each laptop computer produced

generates $$750$ in profit, and each desktop produces $$1000$ in profit. The company wishes

to make the most profit and need to set up the problem to solve to find how many of

each computer to produce.

$($a$)$ Define the choice variables you will use to formulate this problem as a Linear Pro$-$

gram.

$($b$)$ What is the objective function in this Linear Program? Are you maximizing or

minimizing this function?

$($c$)$ List all of the constraints in this problem, be sure to label what the constraints

refer to and the use their units. Hint: you might want to make a table!