Answer to Question #113961 in Operations Research for lois

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? [Hint: let vanilla ice-cream = x]

Answer 1

Try to analyze the condition. For 10 pieces of chocolate ice cream, 20 working and machine hours are required and the profit from them is $45. To provide $45 of profit with vanilla ice cream, you need to produce 18 pieces and spend 18 working and 54 machine hours. Obviously, making chocolate ice cream is more profitable, but at the same time, we need to use all the available hours.

Let x be the amount of vanilla ice cream, and let y be the amount of chocolate.

We compose a system of equations:

3*x+2*y=480;

x+2*y=300;

Solution: x=90; y=105

This is true because if we do not use all available hours, then the income will be less.

Profit: 2.5*x+4.5*y=2.5*90+4.5*105=697.5