Math Problem Solver

QUESTION 3 – LINEAR PROGRAMMING (30 marks)

The Attaran Corporation manufactures two electrical products: portable air conditioners and portable heaters. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each heater must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 240 hours of wiring time are available and up to 140 hours of drilling time may be used. Each air conditioner sold yields a profit of $ 25. Each heater assembled may be sold for a $ 15 profit. Formulate and solve this LP production- mix situation, and find the best combination of air conditioners and heaters that yields the highest profit.

a) Use X1 and X2 to define the variables indicating which variable is X1 and X2 2 Marks

b) Derive the Objective Function in terms of X1 and X2 3 Marks

c) Formulate the Constraints under which the company must operate 7 Marks

d) Graphically illustrate the Feasible Region 4 Marks

e) State the coordinates of the corner points e.g A (2,7), B (12,5) 8 Marks

f) Determine the optimal solution 4 Marks

g) Determine the profit at the optimal solution 2 Marks