Question

Ahmadi, Inc. manufactures laptop and desktop computers. In the upcoming production period, Ahmadi needs to decide how many of each type of computers should be produced to maximize profit. Each computer goes through two production processes. Process I, involves assembling the circuit boards and process II is the installation of the circuit boards into the casing. Each laptop requires 24 minutes of process I time and 16 minutes of process II time. Each desktop requires 8 minutes of process I time and 32 minutes of process II time. In the upcoming production period, 240 minutes are available in process I and 320 minutes in process II. Each laptop costs $1,800 to produce and sells for $2,250. Each desktop costs $600 to produce and sells for $1,000.

Let your decision variables be:

                  X1 = Number of laptops to produce

                  X2 = Number of desktops to produce

a.   Formulate an LP problem to maximize profit. Write your problem formulation.

b.   Graph the constraints and show the region of feasible solutions.

c.   Determine the extreme points of the feasible region.

d.   Find the profit at each extreme point.

e.   Draw the isoprofit line and indicate the optimum point.

f.    Write the problem in the standard form.

g.   Are there any slacks at optimum?

h.   If the selling price per desktop decreases to $700 per unit would there be any change in the optimum solution? If yes, what would be the new optimum solution, and would there be any slack?

i.    Assume the company does not want to produce more than 9 laptops in this production period. Add this constraint to the original problem and show the region of feasible solutions.

j.    Solve the problem as stated in part i and find the optimal solution. Let the profit per Laptop to be $450 and per Desktop to be $100.

k.   Let the selling price of Desktops to be $750 and solve the problem as stated in part i.

l.    Use “Solver” in Excel and solve the original problem from part “a.”

Answer 1