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Answer :
To meet the deadline of painting a house in 2 days, each of Morgan's two assistants must work at a rate of 3/10 of a house per day. The marginal product of the third painter is 75 square feet per hour. The estimated budget for hiring 5 people at $15/hour each for 2 hours of work is $150.
Morgan can paint a house in 5 days, but with the assistance of his two new hires, he needs to complete the painting in 2 days. Let's calculate the rate at which the assistants need to work to meet this deadline. Morgan's rate of painting is 1 house in 5 days, which is 1/5 of a house per day. The combined rate needed to paint the house in 2 days is 1/2 of a house per day. If Morgan's contribution is 1/5, the assistants need to cover 1/2 - 1/5 = 2/5 - 1/5 = 3/5 of the house per day together. If we assume that the assistants work at the same rate, then each assistant must paint at a rate of 1/2 of 3/5 per day, that is 3/10 of a house per day. Thus, the work rate per assistant must equal 3/10 of a house per day.
Example of a linear equation for a painting job: If the setup time is 4 hours plus 1 hour per 1,000 square feet, let x be the number of thousands of square feet to be painted. The total time t in hours is t = 4 + x.
The marginal product of the third painter is the additional amount of area that can be painted by adding the third painter to the group of two. If two painters can paint 200 square feet in an hour and three painters can paint 275 square feet in an hour, the marginal product of the third painter is 275 - 200 = 75 square feet per hour.
For the estimated budget projection, if 5 people are hired at $15 per hour each and work for 2 hours, the budget would be 5 people x $15/hour x 2 hours = $150.
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Rewritten by : Barada
To solve this problem you must apply the proccedure shown below:
1. You have that Morgan can paint the house in about 5 days. Therefore, his rate is:
rate=1/5
2. Then the rate that the two assistants must work for Morgan to meet a deadline of two days is:
2(1/5)+x(2)=1
2/5+2x=1
2x=1-(2/5)
2x=3/5
x=3/(5x2)
x=3/10
The answer is: 3/10
1. You have that Morgan can paint the house in about 5 days. Therefore, his rate is:
rate=1/5
2. Then the rate that the two assistants must work for Morgan to meet a deadline of two days is:
2(1/5)+x(2)=1
2/5+2x=1
2x=1-(2/5)
2x=3/5
x=3/(5x2)
x=3/10
The answer is: 3/10
