Two fragrances A and B are used to make the perfumes Laughte

Two fragrances A and B are used to make the perfumes Laughter and Joy.You require 3 g of fragrance A and 4 g of fragrance B to produce 1 litre of Laughter.One litre of Joy requires 9 g of fragrance A and 6 g of fragrance B.At least 3 litres of Laughter needs to be produced per week.At the beginning of a particular week the company has 27 g of fragrance A and 30 g of fragrance B. Let x and y be the number of litres of Laughter and Joy respectively that are produced per week.

If the profit on 1 l of Laughter is R30 and the profit on 1 l of Joy is R50, express the profit, P, in terms of x and y.

Solution

in a week we produce x litres of laughter and y litres of joy.

Profit from 1L of laughter = 30

Profit from 1L of Joy = 50

Profit from laughter per week = 30x

Profit from Joy per week = 50y

Total profit = 30x+50y

So the profit function P can be determined as;

P = 30x+50y