Problem 1: A production process can make two products, A and B. A requires 2 hours and 1 kilo of mix, whilst B requires 3 hours and 3 kilos of mix. There is an agreement to make at least 3 of A. Profit is £4 for each A and £10 for each B. There are 100 hours per week and 60 kilos of mix available.
In Problem 1, the time constraint is:
A + 3B ≤ 60
A + 2B ≤ 100
2A + 3B ≤ 60
2A + 3B ≤ 100
In Problem 1 the mix constraint is:
A + 3B ≤ 60
A + 2B ≤ 100
2A + 3B ≤ 60
2A + 3B ≤ 100
In Problem 1 the profit function is:
2A + 3B
4A + 10B
10A + 4B
100A + 60B
In Problem 1 the other constraints are:
A ≥ 3, B ≥ 0
A ≤ 3, B ≥ 0
A ≤ 3, B ≤ 0
A ≥ 3, B ≤ 0
For Problem 1, the optimum solution is:
A = 0, B = 33
A = 3, B = 19
A = 40, B = 6.67
A = 50, B = 0
For Problem 1, the maximum profit is:
200.0
202.0
226.7
330.0
In Problem 1, if there is another constraint that B must be at least 10, how many A will be produced?