Answer:
a) Table:
Time required in hours to produce a unit of good
shoe slipper
A machine 1 0.5
B machine 1 1
Worker 2 2
Let x be the number of shoes produced and y be the number of slippers produced in a day.
The mathematical model for the best sales revenue is:
Maximize:
60x + 20y (selling price)
Subject to:
x ≤ 20A (machine A limit)
x ≤ 15B (machine B limit)
2x + 2y ≤ T (worker limit)
where T is the number of hours the workers work in a day.
Also, x and y must be non-negative.
b) To solve the mathematical model, we need to use linear programming. The standard form of the model is:
Maximize:
60x + 20y + 0s1 + 0s2 + 0s3
Subject to:
x − 20A + s1 = 0
x − 15B + s2 = 0
2x + 2y − T + s3 = 0
x, y, s1, s2, s3 ≥ 0
We can use a software or a calculator to find the optimal solution. The solution is:
x = 10
y = 30
A = 10
B = 10
T = 40
s1 = 0
s2 = 0
s3 = 0
Revenue = $2,400
c) The solution means that the factory should produce 10 shoes and 30 slippers in a day to maximize the revenue. Machine A and B should be used for 10 hours each per day. The workers should work for 20 hours to complete the production. The revenue earned per day would be $2,400.
The conclusion is that to maximize the revenue, the factory needs to produce more slippers than shoes. This is because the selling price of slippers is lower than that of shoes, but they require less time and resources to produce. Machine A is more efficient than machine B in producing shoes, but for slippers, both machines have the same efficiency. The workers will work for 12 hours or more, depending on the demand for the products.
Explanation: