An excavating company charges $330 an hour for the use of a backhoe and $550 an hour for the use of a bulldozer. The company employs one operator for 40 hours per week to operate the machinery. If the company wants to bring in at least $18,500 each week from equipment rental, what is the maximum whole number of hours per week can it schedule the operator to use a backhoe?
A) 17 hr
B) 13 hr
C) 14 hr
D) 16 hr
E) 15 hr

Question

Quizplus · Accepted Answer

To maximize the hours the backhoe is used while still meeting the $18,500 weekly income goal, we first calculate the minimum income from the bulldozer to meet the goal. Assuming the bulldozer is used for the remaining hours (40 - x), where x is the number of hours the backhoe is used:1. Bulldozer income: $550 * (40 - x)2. Backhoe income: $330 * xThe total income should be at least $18,500, so we set up the equation:$550 * (40 - x) + $330 * x ≥ $18,500Solving for x gives the maximum hours the backhoe can be used while still meeting the income goal. Calculating the exact value of x and rounding down to the nearest whole number (since we're looking for the maximum whole number of hours) gives us 15 hours.

An Excavating Company Charges $330 an Hour for the Use