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?
and Constraint Graph Space

Answer 1

Let x be the number of vanilla ice creams, and y be the number of chocolate flavoured ice creams. The given problem is a maximization of revenue. The given problem can be represented as

$\text{Maximize}~~ z=2.5x+4.5y\\ \text{subject to}\\ x + 2y \leq 300\\ 3x + 2y \leq 480\\ x, y \geq 0$

From the graph in the above figure, the constraint graph, the points are (0,0), (0,150), (160,0) and (90,105).

The values of z are respectively,

$z = 0; ~z = 675;~ z=400;~z=697.5.$

Therefore, Maximum revenue is 697.5 and the company must manufacture 90 vanilla ice creams and 105 chocolate flavoured ice creams to maximize revenue.