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.

Answer 1

The objective function that can be used to maximize the profit is :

P(a,b)= 15a + 8b.

What is an objective function?

An objective function is a linear representation of the form Z = ax + by, where a, b are constraints and x, y are variables that must be maximized or minimized. The decision variables are variables x and y. The objective function of a linear programming problem is required to find the optimal solution: maximise profit, minimise cost, or minimise resource use, right resource deployment.

The objective function is calculated as:

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 objective profit function is:

P(a,b) = 15a + 8b.

Therefore, the objective function is P(a,b) = 15a + 8b, subject to

a >= 30;  b>= 10;  a+b <= 80.

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