Question

A contractor does two types of repair work, fixing plumbing issues and drywall repair. Due to other obligations, they never want to work more than 14 hours per week on these two tasks. The contractor has determined for every hour they work on fixing plumbing, they need one hour to prepare, and for every hour they work on repairing walls, they need two hours of preparation time. They cannot spend more than 11 hours each week in preparing for the two tasks. If the contractor makes $30 an hour fixing plumbing and $65 an hour repairing walls, how many hours should they work per week at each task to maximize their income?

a. The variables needed to solve the linear programming problem are as follows: x:= Number of hours worked fixing plumbing y:= Number of hours worked repairing drywall I:= Total Income
b. Objective: maximize
c. Subject to: (Hint: Write the constraints line by line. Separate the non-negativity constraints with commas) (Preparation time constraint) (Work time constraint) (Non-negativity constraints)

Answer 1

To maximize their income, the contractor should work a certain number of hours per week at each task. Let's use the variables: x for fixing plumbing and y for repairing drywall. The objective is to maximize income, subject to constraints on preparation time and work time.

Step-by-step explanation:

To maximize their income, the contractor should work a certain number of hours per week at each task. Let's use the variables:

• x: number of hours worked fixing plumbing
• y: number of hours worked repairing drywall
• I: total income

The objective is to maximize the income, so we want to maximize I. The constraints are:

1. Preparation time constraint: x + 2y ≤ 11
2. Work time constraint: x + y ≤ 14
3. Non-negativity constraints: x ≥ 0 and y ≥ 0

Now, we can solve this linear programming problem to find the optimal solution for x and y that maximizes the income I.