What is the area of the triangle?
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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
1.075p to represent “the expected population next year,” which may result from adding p, the current population, to 0.075p, the expected increase in population next year. The expression 1.075p relates the current population to the expected population next year using the expected percent increase.