Question

A manufacturer of hot tubs makes two kinds of hot tubs – Bill and Jane. Bill requires 10 hours of labor and Jane requires 12 hours. Bill needs 50 feet of tubing and Jane needs 40 feet. The manufacturer expects to have 2,000 labor hours and 10,000 feet of tubing available. A single hot tub of type Bill requires 4 pumps; however, type Jane requires 3 pumps. He has 720 pumps at his disposal. Let X= the number of Bill bathtubs and Y= the number of Jane bathtubs manufactured. Which constraint(s) below represent(s) the restriction on tubing?

Group of answer choices
a) 50X+40Y <= 10,000
b) .4X+3Y <= 720
c).Both 50X+40Y <= 10,000 and 5X+4Y <= 1,000 can work.
d).10X+12Y <= 20500
e).5X + 4Y <= 1,000

Answer 1

The correct constraint representing the restriction on tubing is 50X+40Y <= 10,000. This ensures that the manufacturing of the hot tubs does not exceed the available tubing.

Step-by-step explanation:

The constraint representing the restriction on tubing in the manufacturing of two types of hot tubs, Bill and Jane, can be deduced by the amount of tubing required by each. Given that Bill requires 50 feet of tubing and Jane requires 40 feet, the constraint must contain these numbers in relation to the total amount of tubing available, which is 10,000 feet.

Hence, the equation that represents this constraint will use the number of each type of hot tub (X for Bill and Y for Jane) multiplied by their respective tubing requirements and then compare the sum to the total tubing available. This results in the inequality 50X + 40Y <= 10,000 which represents the maximum amount of tubing that can be utilized to produce the hot tubs under the given conditions.

Considering other provided constraints is unnecessary since they relate to labor hours and pumps, not tubing. Therefore, the final answer in two line explanation in less than 200 words: The correct constraint for the restriction on tubing is 50X+40Y <= 10,000. This inequality ensures the manufacturer does not exceed the available 10,000 feet of tubing when producing both types of hot tubs.