Aproduction facility produces metal fasteners, and realizes a profit of $800 per machine per month for 10 machines. each machine requires cooling water to keep it running effectively. management wishes to install more machinery, but the cooling water available cannot keep up with unlimited demand, and adding more machines would cause them all to run more slowly. each additional machine reduces profit by $25 per month. thus with 10 machines, the profit is $8000 (= 800 x 10). for 11 machines the profit is $8525 [= (800 – 25) x 11]. likewise for 12 machines, the profit is $9000 [= (800 – 2(25)) x 12]. determine the optimum number of machines that should be installed to maximize profit.