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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
