Question

A company produces two products, A and B. At least 30 units of product A and at least 10 units of product B must be produced. The maximum number of units that can be produced per day is 80. Product A yields a profit of $15 and product B yields a profit of $8. Let a = the number of units of product A and b = the number of units of product B. What objective function can be used to maximize the profit?

Answer 1

p=15a+8b
is the answer

Answer 2

Let a = units of A produced
Let b = units of B produced

At least 30 units of product A and 10 units of product B are required daily, and the maximum number of units per day should not exceed 80.
Therefore
a ≥ 30
b ≥ 10
a + b ≤ 80

Product A yields a profit of $15 and product B yields a profit of $8.
Therefore the objectve profit function is
P(a,b) = 15a + 8b

Answer:
The objective function is
P(a,b) = 15a + 8b, subject to
a >= 30; b>= 10; a+b <= 80

Create a graph that displays the constraints and calculates maximum profit at the boundary points. The solution region is shaded.
The maximum profit occurs when a=70 and b=10.