Question

You need to make two goods, face masks and gloves (for hospital workers). Each good requires two steps, assembly(x) and sanitization(y). Face masks take 2 hours to assemble and 1 hour to sanitize. Gloves take 1 hour to assemble and 2 hours to sanitize. You have up to 30 hours to make face masks, and up to 24 hours to make gloves. What are the two restraints we'd use in a maximization problem?

Answer 1

Answer:

We would use 12 hours assembly and 6 hours sanitization in a maximization problem

Step-by-step explanation:

Let us make a system of inequalities to solve the problem

Each good requires two steps, assembly(x) and sanitization (y)

∵ Face masks take 2 hours to assemble and 1 hour to sanitize

- Multiply x by 2 and y by 1, then add the products

∴ The face masks take 2x + y hours

∵ You have up to 30 hours to make face masks

∴ 2x + y ≤ 30

∵ Gloves take 1 hour to assemble and 2 hours to sanitize

- Multiply x by 1 and y by 2, then add the products

∴ The gloves take x + 2y hours

∵ You have up to 24 hours to make gloves

∴ x + 2y ≤ 24

Lets solve the system as equations to find the maximum values of x and y

∵ 2x + y = 30 ⇒ (1)

∵ x + 2y = 24 ⇒ (2)

- Multiply (2) by -2

∴ -2x - 4y = -48 ⇒ (3)

- Add (1) and (3)

∴ -3y = -18

- Divide both sides by -3

∴ y = 6

- Substitute the value of y in equation (2) to find x

∵ x + 2(6) = 24

∴ x + 12 = 24

- Subtract 12 from both sides

∴ x = 12

Look to the attached graph of the two inequalities to check the maximum values of x and y

We would use 12 hours assembly and 6 hours sanitization in a maximization problem