Question

QUESTION TWO

A. Fiifi Auto mobile company manufactures cars and trucks. Each vehicle must be processed in the paint shop and body assembly shop. If the paint shop were only painting trucks, then 80 per day could be painted. If the paint shop were only painting cars, then 120 per day could be painted. If the body shop were only producing cars, then it could process 100 per day. If the body shop were only producing trucks, then it could process 100 per day. Each truck contributes GHS60,000 to profit, and each car contributes GHS40,000 to profit. Use linear programming to determine a daily production schedule that will maximize the company’s profits. (10 marks

Answer 1

A.

Linear Programming model is formulated as under:

Let T be the number of Trucks and C be the number of Cars to be produced daily

Total_Profit) Max 60000T+40000C

s.t.

Paint_Shop) (1/80)T+(1/120)C <= 1 or, 3T+2C<=240

Body_Shop) (1/100)T+(1/100)C <= 1 or, 1T+1C<=100

T, C >= 0

Solution by LINDO is as follows:

Lingo 18.0 - Solution Report - Lingo1 File Edit Solver Window Help 2 Lindo Model - Lingo1 Solution Report - Lingo1 Global optimal solution found. Objective value: Infeasibilities: Total solver iterations: Elapsed runtime seconds: Total_Profit) Max 60000T+40000C 4800000. 0.000000 1 0.04 s.t. Paint_Shop) 3T+2C<=240 Model Class : LP Body_Shop) 1T+10<=100 Total variables: Nonlinear variables: Integer variables: 2 0 0 Total constraints: Nonlinear constraints: 3 0 Total nonzeros: Nonlinear nonzeros: 6 0 Variable Value 80.00000 0.000000 Reduced Cost 0.000000 0.000000 с Row TOTAL PROFIT PAINT SHOP BODY SHOP Slack or Surplus 4800000. 0.000000 20.00000 Dual Price 1.000000 20000.00 0.000000

.

Optimal daily production mix:

Trucks = 80

Cars = 0

Daily profit = 4,800,000