The profit function is P = 50x + 80y, where x represents the number of chairs and y represents the number of sofas. Using the values of the profit function at the vertices, find how many chairs and sofas the manufacturer should produce to earn that profit. (0, 0) P = 0 (0, 15) P = 1,200 (6, 12) P = 1,260 The manufacturer can earn a maximum profit of $ by producing chairs and sofas.

Answer: Given the 3 choices in the problem, the greatest profit would be for the final pair (6, 12).

If you input 6 for x in the function and 12 for y in the function, you will get an output profit value of 1260.
P = 50(6) + 80(12)
P = 300 + 960

On these types of problems, there are generally multiple constraints that you have to be aware of. One of the vertices of the possible areas must be (6, 12).