Part a Given the following multivariate function 50 18X 10

Part a

Given the following multivariate function: 50 + 18X + 10Z – 5XZ – 2X 2

• Determine the values of X and Z that maximize the function.

Part b

Given the following Total Revenue function: TR = $100,000Q – 10Q2

• Determine the output rate that will maximize total revenue.

• Calculate the dollar amount of total revenue at this rate of output

Part A - Multivariate analysis should be put under Calculus. Standard Economic theory doesn\'t deal with multivariate or Partial derivatives.

Part - B

TR = 100,000Q - 10Q²

TR is maximized when dTR / dQ = 0

100,000 - 20Q = 0

20Q = 100,000

Q = 100,000 / 20 = 5,000

When Q = 5,000, TR = $[(100,000 x 5,000) - (10 x 5,000 x 5,000)]

= $[500,000,000 - 250,000,000] = $250,000,000