Let the number of tennis rackets and cricket bats manufactured by factory be x and y respectively.
Here, profit is the objective function z.
z = 20x + 10y …(i)
We have to maximise z subject to the constraints
1 ×5x + 3y ≤ 42 …(ii) [Constraint for machine hour]
3x + y ≤ 24 …(iii) [Constraint for Craft man’s hour]
x≥0
y≥0
[Non-negative constraint]
Graph of 3x + y ≤ 24 is the part of Ist quadrant in which origin lie
Hence, shaded area OACB is the feasible region.
For coordinate of C equation 1 × 5x + 3y = 42 and 3x + y = 24 are solved as
Now value of objective function z at each corner of feasible region is
Therefore, maximum profit is Rs200, when factory makes 4 tennis rackets and 12 cricket bats.