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A small company manufactures three different electronic components for computers. Component A requires 2 hours of fabrication and 1 hour of​ assembly; component B requires 3 hours of fabrication and 1 hour of​ assembly; and component C requires 2 hours of fabrication and 2 hours of assembly. The company has up to ​labor-hours of fabrication time and ​labor-hours of assembly time available per week. The profit on each​ component, A,​ B, and​ C, is​ $7, $8, and​ $10, respectively. How many components of each type should the company manufacture each week in order to maximize its profit​ (assuming that all components manufactured can be​ sold)? What is the maximum​ profit?

Respuesta :

MrRoyal

The maximum​ profit of the company is #5600

How to determine the maximum profit​?

Let fabrication be represented with x and assembly be y.

The given parameters can be represented as follows:

        x     y    

A        2     1     7

B        3     1     8

C        2     2    10

      1100    900

From the above table of values, we have:

Maximize P = 1100x + 900y

Subject to

2x + y ≤ 7

3x + y ≤ 8

2x + 2y ≤ 10

x, y ≥ 0

Next, we solve the system of inequalities using a graphing calculator.

From the graphing calculator, the feasible coordinates are:

(x,y) = (1,5), (2,3) and (1.5,3.5)

Substitute these values in P = 1100x + 900y

So, we have:

P = 1100 * 1 + 900 * 5 = 5600

P = 1100 * 2 + 900 * 3 = 4900

P = 1100 * 1.5 + 900 * 3.5 = 4800

Hence, the maximum​ profit is 5600

Read more about maximum​ functions at:

https://brainly.com/question/14381991

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