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

x - quantity vanilla ice-cream;

y - quantity chocolate ice-cream.

$2.50x+4.50y \to max;$

$1x+2y=300$

$3x+2y=480;$

$x=300-2y;$

$3×(300-2y)+2y=480;$

$900-6y+2y=480;$

$420=4y;$

$y=105;$

$x=300-2×105=90;$

$2.50×90+4.50×105=225+472.5=\$ 697.5;$

Answer: $ 697.5 - maximum revenue, 90 a portion vanilla ice-cream, 105 a portion chocolate ice-cream.