Question

A television set manufacturing firm has to decide on the mix of color and black-and-white TVs to be produced. A market research indicates that, at most, 2000 units and 4000 units of color and black-and-white TVs can be sold per month. The maximum number of man-hours available is 60,000 per month. A color TV requires 20 man-hours and a black-and-white TV requires 15 man-hours to manufacture. The unit profits of the color and black-and-white TVs are $60 and $30, respectively. It is desired to find the number of units of each TV type that the firm must produce in order to maximize its profit. Formulate the problem as a linear program.

Answer 1

Answer:

Objective Function,  $Max P =60c+30b$

Subject to the Constraints

$0$

$0$

$20c+15b\leq 60000$

Step-by-step explanation:

Let the number of black t.v. produced =b

Let the number of colored t.v. produced =c

at most, 2000 units of color t.v. can be sold i.e. $c\leq 2000$

at most 4000 units of black-and-white TVs can be sold i.e. $b\leq 4000$

Total man hours per product = Number of Units X Man Hour Per Unit

A color TV requires 20 man-hours  = 20c

A black-and-white TV requires 15 man-hours =15b

Since Maximum number of man Hours is 60000 hours

$20c+15b\leq 60000$

The unit profits of the color TV is $60, therefore total profit =60c

The unit profits of the black-and-white TVs $30, respectively, therefore total profit =30b

Since we are to maximize profit, the Objective Function, $Max P =60c+30b$