Question

An electronics firm manufactures two types of personal computers (PC), a desktop model and a laptop model. The production of a desktop computer requires a capital expenditure of $400 and 40 hours of labor. The production of a laptop computer requires a capital expenditure of $250 and 30 hours of labor. The firm has $20,000 capital and 2,160 labor-hours available for production of desktop and laptop computers. Each desktop computer contributes a profit of $320 and each laptop computer contributes a profit of $220.

What are the corner points of the feasible region if we want to maximize the profit?

(a) (50, 0),(30, 32),(0, 72) ;

(b) (50, 0),(54, 0),(30, 32) ;

(c) (0, 80),(0, 72),(30, 32) ;

(d) (0, 0),(50, 0),(30, 32),(0, 72) ;

(e) (0, 0),(50, 0),(0, 72) ;

What are the decision variables if we want to maximize the profit?

(a) x1, x2 and x3 ;

(b) number of desktop and number of laptop to be made ;

(c) x and y ;

(d) x, y and z ;

(e) x1 and x

Answer 1

Part A

Let, the number of desktop to be made is x

Let, the number of laptop to be made is y

Production of a desktop computer requires $400 captital and 40 hours of labour

Production of a laptop computer requires $250 captital and 30 hours of labour

Capital required to produce x desktop computers and y laptop computers is

Total capital available with the firm is $20000 implies

No of hours of labour required to produce x desktop computers and y laptop computers is

Total number of hours of labour available with the firm is 2160 implies

Also, the values of x and y are greater than or equal to 0

The profit function is

Plot the above inequalities.

The region OABC is a the feasible region and the corner points of the region R are (0,0), (50,0), (30,32) and (0,72)

Hence, the answer is Option D

Part B

The decision variables are the number of desktop and number of laptop to be made

Hence, the answer is Option B