Question

Write the constraint below as a linear inequality. A canoe requires 9 hours of fabrication and a rowboat 5 hours. The fabrication department has at most 91 hours of labor available each week. Let x be the number of canoes and let y be the number of rowboats.

a) 5x+9y≤ 91
b) 9x+5y ≤ 91
c) 9x+5y ≥ 91
d) 5x+9y≥ 91

Answer 1

The correct linear inequality representing the constraints on the fabrication time for canoes and rowboats, given the limited labor hours, is 9x + 5y ≤ 91.

Step-by-step explanation:

To write the constraint as a linear inequality, we need to consider the time it takes to fabricate each canoe and rowboat as well as the total hours available for fabrication work. Given that a canoe requires 9 hours of fabrication (x) and a rowboat requires 5 hours (y), and the department has at most 91 hours of labor available, the inequality would be the total hours spent on fabricating canoes and rowboats cannot exceed the available labor hours.

9x + 5y ≤ 91 is the correct linear inequality, where x is the number of canoes and y is the number of rowboats. This inequality ensures that the total combined hours spent fabricating canoes and rowboats do not exceed 91 hours.