Question

The Super-warm Company produces two electric heaters (products A and B) that require both heating elements and electrical components. The owner currently determines how many units of each product to be produced so as to maximize the profit. For each unit of product A, 3 units of heating elements and 1 unit of electrical components are required. For each unit of product B, 1 unit of heating elements and 2 units of electrical components are required. The company has 750 units of heating elements and 600 units of electrical components. Each unit of product A, up to 130 units, gives a profit of $30, and each unit of product B gives a profit of $20. Any excess over 130 units of product A brings no extra profit, so such an excess has been ruled out.

a) Formulate a Linear Programming model for this problem.

b) Use the graphical method to solve this model. What is maximum total profit?

Answer 1

​​​​​​a)

Let the number of units of product A =x₁

Let the number of units of product B =x₂

Objective function: Maximize Z =30x₁ + 20x₂

Constraints:

x₁ 130 (or x₁ + 0x₂ 130);

	A	B	Total
Heating elements	3	1	750
Electrical components	1	2	600

3x₁ + x₂ 750;

x₁ + 2x₂ 600;

x₁ 0; x₂ 0

b)

I'm the above graph,

Horizontal axis is x₁

Vertical axis is x₂

Red line equation is: x₁ =130

Green line equation is: 3x₁ + x₂ =750

Blue line equation is: x₁ + 2x₂ =600

The maximum value of the objective function is Z =8,600 and it occurs at the point B(130, 235).

So, the number of units of product A =x₁ =130 and the number of units of product B =x₂ =235.

Maximum total profit =$8,600