Question

1. A small furniture manufacture producer tables and chairs.  Each product must go through three stages of the manufacturing process:

Each table requires 4 hours of assembly, 3 hours of finishing and 1 hour of inspection

Each chair requires 3 hours of assembly, 2hours of finishing and 2 hours of inspection

The selling price per table is $140 while the selling price per chair is $90

Currently, each week there are 220 hours of assembly time available, 160 hours of finishing time, and 45 hours of inspection time.

Assume that one hour of assembly time costs $.00; one hour of finishing time costs $6.00; one hour of inspection time costs $4.50.

Linear programming is to be used to develop a production schedule.

Let:      T=number of tablets produced each week

            C=number of chairs produced each week

Which of the following expression would be the objective function of this LP problem?

1. Max 140T+90C
2. Max 97.5T+54C
3. Max T+C
4. Min 42.5T+36C

Answer 1

Let:      T=number of tablets produced each week

            C=number of chairs produced each week

The objective function of any business is to increase the profit while minimizing the cost

Fron the given data:

Cost for assembling = number of hours of assembling per week * cost per hour

Cost for Finishing = number of hours of finishing per week * cost per hour

Cost for inspection = number of hours of inspection per week * cost per hour

and

Selling price of each table = 140

Selling price of each Chair = 90

Total selling price on tables = 140 * T

Total selling price on chairs = 90 * C

So,Profit per week (z) = 140T + 90C - 42.5T - 36C = 97.5T + 54C

Objective function :

To maximize Z = 97.5T + 54C

Answer:B

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