A medical clinic performs three types of medical tests that use the same machines. Tests A, B, and C take 15 minutes, 30 minutes, and 1 hour, respectively, with respective profits of $90, $120 and $150. The clinic has 4 machines available. One person is qualified to do test A, two to do test B, and one to do test C. If the clinic has a rush of customers for these tests, how many of each type should it schedule in a 9 - hour day to maximize its profit? Round your profit to the nearest dollar and another answers - to the nearest whole number.
A) 36 A tests; 36 B tests; 36 C tests; maximum profit $12,960
B) 36 A tests; 36 B tests; 18 C tests; maximum profit $12,960
C) 36 A tests; 36 B tests; 9 C tests; maximum profit $8,910
D) 36 A tests; 18 B tests; 9 C tests; maximum profit $6,750
E) 18 A tests; 18 B tests; 9 C tests; maximum profit $5,130

Question

A medical clinic performs three types of medical tests that use the same machines. Tests A, B, and C take 15 minutes, 30 minutes, and 1 hour, respectively, with respective profits of $90, $120 and $150. The clinic has 4 machines available. One person is qualified to do test A, two to do test B, and one to do test C. If the clinic has a rush of customers for these tests, how many of each type should it schedule in a 9 - hour day to maximize its profit? Round your profit to the nearest dollar and another answers - to the nearest whole number. ​
A) 36 A tests; 36 B tests; 36 C tests; maximum profit $12,960
B) ​36 A tests; 36 B tests; 18 C tests; maximum profit $12,960
C) ​36 A tests; 36 B tests; 9 C tests; maximum profit $8,910
D) ​36 A tests; 18 B tests; 9 C tests; maximum profit $6,750
E) 18 A tests; 18 B tests; 9 C tests; maximum profit $5,130

Quizplus · Accepted Answer

Given the constraints, the clinic can maximize its profit by utilizing all machines and personnel efficiently. Each machine can operate for 9 hours a day, totaling 36 hours of machine time. Test A takes 15 minutes (0.25 hours), Test B takes 30 minutes (0.5 hours), and Test C takes 1 hour. The clinic can perform 36 A tests (9 hours / 0.25 hours each), 36 B tests (18 hours / 0.5 hours each, with two machines/personnel), and 9 C tests (9 hours / 1 hour each) in a day. The profit calculation is (36*$90) + (36*$120) + (9*$150) = $3240 + $4320 + $1350 = $8910.

A Medical Clinic Performs Three Types of Medical Tests That