As a supervisor of a production department, you must decide the daily production

Question

As a supervisor of a production department, you must decide the daily production quantity of a certain product that has two models, the Deluxe and the Special. The company sells the Deluxe model for $18 per unit and the Special model for $15 per unit. It costs $6 and $5 to produce each Deluxe model and Special model, respectively Each model goes through two phases in the production process, and there are only 100 hours available daily at the construction stage and only 80 hours available at the finishing and inspection stage. Each Deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time. Each Special model requires 15 minutes of construction time and 15 minutes of finishing and inspection time. The company has also decided that the Special model must comprise at least 40 percent of the production total What is an appropriate objective function for maximizing the total profit? Maximize 12D 10S Maximize 18D 15S Maximize 10OD 80S Minimize 6D+5S Refer to the statement in Question 1. What is an appropriate constraint for the construction time? 20D15S s 100 20D15Ss 6000 20D 15S2100 20D15S 2 6000 Refer to the statement in Question 1. What is an appropriate constraint for the finishing time? 10D15S s 80 5D1OS 2 100 10D15S 2 100 10D15S s 4800 Refer to the statement in Question 1. What is an appropriate constraint for the production quantity requirement? D+S s 40% O D 4096 (D + S) 0.4 D 20.6 S o s 40% (D + S)

Explanation / Answer

1.

A

Working note:

It is a profit maximization problem. Then:

Maximization = (Price – variable cost)*D + (Price – variable cost)*S

Maximization = (18-6)*D + (15-5)*S

Maximization = 12D + 10*S

2.

B

Working note:

Construction stage time for deluxe model = 20 minutes

Construction stage time for special model = 15 minutes

Maximum time = 100 hours or 6000 minutes

So,

20D + 15S 6000

3.

D

Working note:

Finishing stage time for deluxe model = 10 minutes

Finishing stage time for special model = 15 minutes

Maximum time = 80 hours or 4800 minutes

So,

10D + 15S 4800

4.

D

Working note:

Total output = S+D

Constraint: Special model should be at-least 40% of the total models.

Then,

S 40% *(S+D)

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