Page 83 - Mathematics_Form_3

Linear programming

a cost of 18,000 shillings per hour. The company has received an order of
204 units of the SMALL product, 690 units of the MEDIUM product, and
330 units of the LARGE product.

(a) Formulate a linear programming problem for minimizing the cost.
(b) How many hours should be given to each plant in order to satisfy the
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order at the least cost?
14. A doctor advises that in order to obtain an adequate supply of vitamins A
and C, a patient should consume portions of food 1 and food 2. The number
of units of vitamin A and vitamin C are given in the following table.

Nutrients
Food Vitamin A Vitamin C
F 1 3 3
F 1 4
2
The doctor prescribes a minimum of 9 units of vitamin A and 18 units of
vitamin C. What are the least numbers of portions of food 1 and food 2 that
will fit the doctor’s prescription?

15. A bread dealer wants to buy up to 100 loaves of bread. White bread costs
2,500 Tanzanian shillings per loaf while brown bread costs 3,500 Tanzanian
shillings per loaf. The dealer can spend up to 300,000 shillings. The profit
on a loaf of white bread is 1,000 shillings and that of brown bread is 1,200
shillings. How many loaves of each type should he buy to get a maximum
profit? some constraints defined over the

Mathematics for Secondary Schools 1. Linear programming is a 4. Constraints are inequalities or
Chapter summary
set of feasible solutions.
mathematical method for
determining the best possible
equations which connect the
outcome in problems that can be
decision variables under certain
modelled using linear equations
restrictions or limitations.
and inequalities.
5. A feasible region is a set of all
possible solutions of the linear
2. Decision variables are unknown
programming problem.
quantities that decide the output
of a linear programming problem.
values of the decision variables
3. An objective function is a linear 6. An optimal solution is a set of
function whose value is to be either for which the objective function
minimized or maximized subject to attains its optimal value.

76 Student\s Book Form Three

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