Final answer:
The answer includes an explanation of the paint job estimation program, including how to calculate labor hours, the marginal product of a third painter, and how to express cost in a linear equation with a fixed rate plus a per-hour rate.
Step-by-step explanation:
Paint Job Estimation Program
The painting company has determined that for every 115 square feet of wall space, one gallon of paint and eight hours of labor are needed. This company charges $18.00 per hour for labor. In a program designed to estimate the cost of a paint job, we consider several inputs and outputs. The user inputs the number of rooms, the price of paint per gallon, and the square feet of wall space in each room. The desired outputs are the number of gallons of paint required, the hours of labor required, the cost of the paint, the labor charges, and the total cost of the painting job. These outputs are calculated through program methods and then displayed to the user.
Calculating the total hours of labor required for a painting job can be visually represented by a linear equation, based on the information provided: the equation would be L = 4 + (S / 1000), where L represents the total labor hours and S represents the total square feet to be painted. The four hours are the setup time, and the quotient of S over 1000 represents the painting time per square foot.
The marginal product of the third painter is determined by comparing the output with two painters to the output with three. If two painters can paint 200 square feet in an hour and three painters can paint 275 square feet, the marginal product of the third painter is the difference, which is 75 square feet per hour.
An example of a service charging a fixed rate plus a per-hour rate is provided by Aaron's Word Processing Service. The total cost equation can be expressed as C = 31.50 + 32h, where C is the total cost to the customer, and h is the number of hours required to complete the job