1. Daniel Dement is the supervisor of production at ABC Inc. in Louisville KY. D

Question

1. Daniel Dement is the supervisor of production at ABC Inc. in Louisville KY. Daniel must decide the optimal daily production mix of a certain product that has two models, the Deluxe and the Special. The profit on the Deluxe model is $15 per unit and the Special's profit is $11 per unit. Each model goes through three departments in the production process, construction, finishing and inspection. There are only 100 hours available daily in the construction department, only 80 hours available in finishing and 75 hours in inspection. Each Deluxe model requires 20 minutes of construction time, 10 minutes of finishing time and 8 minutes of inspection time. Each Special model requires 15 minutes of construction time, 15 minutes of finishing time, and 10 minutes of inspection time.

The company has also decided that the Special model must comprise at least 40 percent of the production total.

Write the linear programming formulation for this problem.

Explanation / Answer

Lets say x be the number of units of Deluxe and y be the number of units of Special

Number of Special must be at least 40% of total production

Total production=x+y

hence x>=0.4*(x+y)

or 0.4y-0.6x<=0

Profit =15*x+11*y

Number of construction hours required=x*20+15*y

Given number of construction hours is maximum of 100 hours=6000 minutes

hence x*20+y*15<=6000

Number of finishing hours required=x*10+15*y

Given number of finishing hours is maximum of 80 hours=4800 minutes

hence x*10+y*15<=4800

Number of inspection hours required=x*8+10*y

Given number of inspection hours is maximum of 75 hours=4500 minutes

hence x*8+y*10<=4500

We have to maximize profit hence maximize 15*x+11*y subject to

x*20+y*15<=6000

x*10+y*15<=4800

x*8+y*10<=4500

0.4*y-0.6*x<=0

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