Acompany 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?

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

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.

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