A factory manufactures three products and has an annual profit given by

where x, y, and z represent the number of units manufactured (in units of 10,000) of products X, Y, and Z, respectively, in the year. In order to meet the demands of its current contracts, the factory is required to manufacture a combined total of 120,000 units of X and Y.

a. Determine the optimal values of x, y, and z.

b. Determine how the maximum profit could change if the factory restricts orders such that the total combined units of X and Y is 100,000.

Transcribed Image Text:

P(x, y, z) = 6x +8y + 4z-0.4x²-y² - 2²