Tengo is asking again about his profit for his lawn mowing service. Recall that profit P(x) is equal to revenue R(x) minus cost C(x), and revenue is x times the price p(x); basically P(x) = R(x) − C(x) = x · p(x) − C(x).
He had to buy $100 of equipment to start his service, and it costs $4 per lawn for fuel. He initially charged $20 per lawn, but wants to make a discount by decreasing this rate by $0.1 for every lawn he is servicing. He thinks this discount will keep customers happy and will make them want to spread the word about his service as it gets them a discount.

Find Tengo’s cost, price, and revenue functions in terms of x, which represents the number of lawns he is servicing. Then find Tengo’s profit function in terms of x. When he is cutting 50 lawns, what is his marginal and average profit? Explain why he should or should not be servicing 51 lawns instead of 50 lawns using this information.

How many lawns does Tengo need to cut in order to maximize his profit (You can use a graph to find the answer to this)? What is his maximum profit? Using marginal profit, explain why this is a maximum profit.