Answer to Question #113633 in Algebra for Malia Losalu

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

• For the optimum conditions assume all the work force is employed in the manufacturing process.
• Therefore, if the produced vanilla ice cream = x & the chocolates = y

Then, considering labour workforce

$\qquad\qquad \begin{aligned} \small x + 2y &= \small 300 \end{aligned}$

And considering the machine workforce

$\qquad\qquad \begin{aligned} \small 3x + 2y &= \small 480 \end{aligned}$

Then solving these equations

$\qquad\qquad \begin{aligned} \small x &= \small \bold{ 90}\\ \small y &= \small \bold{105} \end{aligned}$

Therefore, at the optimum conditions, the company could produce 90 Vanilla ice-cream & 105 chocolate ice-cream which can generate a maximum revenue of $2.5*90 + $4.5*105 = $697.5.