Part $2-$ Using Solver for Linear Programming

For these cases be sure to provide your solver solutions showing the parametrs of solver.

Case $3.$ Dalton Manufacturing produces two popular grades of commercial carpeting among its many

other products. In the coming production period, Dalton needs to decide how many rolls of each grade

should be produced in order to maximize profit. Each roll of Grade I carpet uses $50$ units of synthetic

fiber, requires $25$ hours of production time, and needs $20$ units of foam backing. Each roll of Grade II

carpet uses $40$ units of synthetic fiber, requires $28$ hours of production time, and needs $15$ units of foam

backing. Each roll of Grade I carpet sells for $$1,200$ and costs $$1,000,$ and each roll of grade II carpet

sells for $$910$ and costs $$750$ to produce. In the coming production period, Dalton has $3000$ units of

synthetic fiber available for use. Workers have been scheduled to provide at least $1600$ hours of

production time. The company has $1000$ units of foam backing available for use.

Let your decision variables be:

$x1=$ Number of rolls of Grade I carpet to make

$x2=$ Number of rolls of Grade II carpet to make

a$.$ Formulate an LP problem to determine the highest profit.

Write your objective function and the constraints.

b$.($optinal$)$ Graph the constraints and show the region of feasible solutions.

Determine the optimum solution and give the values of the decision variables as well as the slacks.

c$.$ Using Excel's Solver, solve the problem and write the solution values below.

Give the maximum profit, values of the decision variables and slacks.

d$.$ The selling price of Grade I carpet has gone up to $$2,000$ per roll.

Solve the new problem with solver and provide the new values of the solution.