7. [10 points] Maximum Profit: A furniture store can sell 40 chairs per week at a price of $80 each. The manager estimates that for each $5 price reduction she can sell five more chairs per week. The chairs cost the store $30 each. If z stands for the number of $5 price reductions, find the price of the chairs and the quantity that maximize the profit. [Hint: Find the price p(r) and the quantity sold q(r) as functions of z. Revenue is price times quantity, cost is the cost per item times quantity, profit is revenue minus cost].