Sandy edge is president of Edge File Works, a firm that manufactures two types of metal file cabinets.

The demand for the two$-$drawer model is $650$ cabinets per week; demand for the three$-$drawer cabinet is

$400$ per week. Edge has a weekly operating capacity of $1,600$ hours, with the two$-$drawer cabinet taking

$1\mathrm{.}5$ hours to produce and the three$-$drawer cabinet requiring $2$ hours. Each two$-$drawer model sold yields

a $$12$ profit, and the profit for the three$-$drawer model is $$14.$ Edge has listed the following goals:

Goal $1$: Attain a profit as close to $$12,000$ as possible each week.

Goal $2$: Avoid underutilization of the firm's production capacity.

Goal $3$: Sell as many two$-$ and three$-$drawer cabinets as the demand indicates.

Set up and solve this problem as a goal programming model using following methods$-$

a$.$ Consider goal $1$ to be $3$ time more important than goal $2,$ and $4$ times more important than goal

Solve using weighted method.

b$.$ Consider the $3$ goals to be equally important. Solve using weighted method.

c$.$ Consider goal $1$ to be your top priority $($Rank $1),$ goal $2$ to be second priority $($Rank $2)$ and goal $3$

to be third priority $($Rank $3).$ Solve using Rank method.