Page 77 - Mathematics_Form_3

Linear programming

product A is sold for Tshs 400,000 and product B for Tshs 600,000, how many
units of each product should be manufactured to obtain maximum gross income?
Solution
The given information are summarized as shown in the following table:
FOR ONLINE READING ONLY
Wood Plastic Steel Profit (Tshs)
Product A 1 3 2 400,000
Product B 3 4 1 600,000
Maximum
requirements 24 36 18
Let: x be the number of units of product A to be manufactured, and
y be the number of units of product B to be manufactured.

Thus, the objective function is given by;
Maximize f (x, y) = 400000x + 600000y

Subject to: x + 3y ≤ 24
3x + 4y ≤ 36
2x + ≤ 18
y
x ≥ 0, y ≥ 0
The graph of the constraints is shown in the following figure.

y

10 E(0, 8) D(2.4, 7.2)

Mathematics for Secondary Schools -2 6 x=0 2 4 y=0 6 C(7.2, 3.6) 12 x
8
2x + y = 18

x + 3y = 24
4
Feasible region
2

B(9, 0)
A(0, 0)
3x + 4y = 36
8
10
0
-2
The corner points and values of the objective function at the corner points are
shown in the following table.

70 Student\s Book Form Three

18/09/2025 09:59:11
MATHEMATIC F3 SB.indd 70
MATHEMATIC F3 SB.indd 70 18/09/2025 09:59:11