Answer to Question #114370 in Operations Research for shimran

Question

A company manufactures two kinds of ice-cream. The vanilla ice-cream sells for $2.50 each while the chocolate flavour ice-cream sells for $4.50 cents each. It costs the company 1 labour hour to make the vanilla flavour ice-cream and 2 labour hours to make the chocolate flavour ice-cream. The company has a total of 300 labour hours available. It costs the company 3 machine hours for the vanilla ice-cream and 2 machine hours for the chocolate ice-cream. The company has a total of 480 machine hours available. How much of each type of ice-cream should the company produce to maximise revenue? What is the maximum revenue?

Answer 1

Let vanilla ice creams produced be x and chocolate ice cream be represented by y.

So,Max Z=2.50x+4.50y

subject to:

x+2y ≤ 300 (Labour hour constraint)

3x+2y≤400 (Machine hour constraint)

x≥0,y≥0

Now,plotting it on graph:

Labour hour constraint is red line and Machine hour constraint is blue line.

Now finding values at the feasible points.

Points Value

(0,0) 0

(160,0) 400

(90,105) 697.5

(0,150) 675

So,90 vanilla and 105 chocolate ice cream to be made for obtaining maximum revenue which is $697.5