(Table: Variable Costs for Lawns) Use Table: Variable Costs for Lawns.During the summer,Alex runs a lawn-mowing service,and lawn-mowing is a perfectly competitive industry.Assume that costs are constant in each interval;so,for example,the marginal cost of mowing each of the lawns from 1 through 10 is $10.Also assume that he can only mow the quantities of lawn given in the table (and not numbers in between) .His only fixed cost is $1,000 for the mower.His variable costs include fuel,his time,and mower parts.If the price for mowing a lawn is $70,how much is Alex's total cost at the profit-maximizing output?

A) $3,500
B) $2,800
C) $2,100
D) $1,500

Question

Justin Zendejas · Accepted Answer

Final Answer : B, Explanation :  To find the profit-maximizing output, we need to find the quantity of lawns where the marginal cost is equal to the price. In this case, the price is $70. Looking at the table, we see that the marginal cost of mowing the 20th lawn is $70. Therefore, the profit-maximizing output is 20 lawns.To calculate Alex's total cost at this output, we need to add up his fixed cost and variable costs for mowing 20 lawns. His fixed cost is given as $1,000. To calculate the variable costs, we need to add up the costs for mowing 20 lawns, which are:- $10 for the first 10 lawns- $20 for the next 5 lawns- $30 for the next 3 lawns- $40 for the next 1 lawnTotal variable costs for 20 lawns = $10(10) + $20(5) + $30(3) + $40(1) = $100 + $100 + $90 + $40 = $330Total cost = fixed cost + variable costs = $1,000 + $330 = $1,330Therefore, Alex's total cost at the profit-maximizing output of 20 lawns is $1,330. However, since the question asks for the cost of mowing a lawn, we divide the total cost by 20 to get the cost per lawn: $1,330/20 = $66.5 per lawn.Since the price for mowing a lawn is $70, Alex's profit per lawn is $70 - $66.5 = $3.5.Therefore, the total profit at the profit-maximizing output of 20 lawns is $3.5 x 20 = $70.To summarize:Total cost at profit-maximizing output of 20 lawns = $1,330Cost per lawn = $1,330/20 = $66.5 per lawnProfit per lawn = $70 - $66.5 = $3.5 per lawnTotal profit at profit-maximizing output of 20 lawns = $3.5 x 20 = $70.

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