IV. Extrema with D-Test, and Optimization 15) Maximizing Profit (optimizing functions with several variables): A company sells farm equipment in America and Europe, charging different prices in the two markets. The price function for harvester sold in America is p = 80 – 0.2x, the price function for harvester sold in Europe is p = 64 – 0.1y (both in thousands of dollars), where x and y are the numbers sold per day in America and Europe, respectively. The company's cost function is C=100 +12(x+y) thousand dollars. a. Find the company's profit function P(x, y). d. Find how many harvesters should be sold in each market to maximize profit. Also find the price for each market.

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.