Grade 11 Tutorials - Maths Excellence

Question 10
Vitamins B and E are vital ingredients of two types of
health drinks, Energex and Vitagex
• You require 3 g of Vitamin B and 4 g of Vitamin E to produce 1 litre of Energex
• You require 9 g of Vitamin B and 6 g of Vitamin E to produce 1 litre of Vitagex
• The company has 27 g of Vitamin B and 30 g of Vitamin E per day
The above information is summarized in the table below:
Ingredients Energex Vitagex Maximum grams
Vitamin B 3 9 27
Vitamin E 4 6 30
• Furthermore at least 3 litres of Energex needs to be produced per day.
Let x and y be the number of litres of Energex and Vitagex respectively that are produced per day.
10.1 State algebraically, in terms of x and y, the constraints that apply to this problem for a day.
10.2 Represent the constraints graphically on the graph paper provided and shade the feasible region.
10.3 If the profit on 1 l of Energex is R30 and the profit on 1 l of Vitagex is R50, express the
profit, P, in terms of x and y.
10.4 Determine, by making use of a searchline, how many litres of each health drink must be
produced in a day to ensure a maximum profit.
10.5 Calculate the maximum possible profit.
Grade 11 - 20 - Tutorials