Question

A bicycle shop assembles bicycles and unicycles. The bikes need 2 wheels, require 4 hours of labor to assemble, and bring in $300 of profit. The unicycles only need 1 wheel, require 1 hour of labor, and generate $100 of profit. The shop has 60 wheels on hand and 80 hours of available labor. The owner wishes to maximize profit on the assumption that he can sell all the units he assembles. Let B = number of bikes to be assembled & U = number of unicycles to be assembled. Which of the following represents the constraints for this problem?

a. B ≥ 0, U ≥ 0, 2B + U ≤ 60, 4B + U ≤ 80
b. B ≥ 0, U ≥ 0, 4B + 2U ≤ 60, 2B + U ≤ 80
c. B ≥ 0, U ≥ 0, 4B + U ≤ 60, 2B + 2U ≤ 80
d. B ≥ 0, U ≥ 0, 2B + 2U ≤ 60, 4B + U ≤ 80

Answer 1

The correct constraints for maximizing profit in the bicycle shop scenario are B ≥ 0, U ≥ 0, 2B + U ≤ 60 (for wheels), and 4B + U ≤ 80 (for labor).

Step-by-step explanation:

The question revolves around finding the constraints for a linear programming problem in which a bicycle shop is seeking to maximize profit by deciding the number of bicycles (B) and unicycles (U) to assemble given certain resource limitations.

Since bicycles require 2 wheels each and 4 hours of labor, and unicycles require 1 wheel each and 1 hour of labor, the constraints related to wheels and labor can be expressed as 2B + U ≤ 60 (wheels constraint) and 4B + U ≤ 80 (labor constraint), respectively. Additionally, both B and U must be greater than or equal to zero since you cannot assemble a negative number of bikes or unicycles. Therefore, the correct set of constraints for the problem indeed is a. B ≥ 0, U ≥ 0, 2B + U ≤ 60, 4B + U ≤ 80.