A retail outlet sells two types of riding lawn mowers, the prices of which are p, and p2. Using the revenue function below, find p₁ and p₂, in dollars, so as to maximize total revenue. STEP 1: R = 855p1 + 975p2 + 1.5p1P2 - 1.5p12-P22 Determine the partial derivatives. Rp₁ (P1, P2) = P1 Rp2(011 P2) = STEP 2: Set the partial derivatives equal to zero to produce a system of equations. R (2) = = 0 Rp2 (P1 P2) = = 0 STEP 3: Solve the system. P1 P2 = $ $

bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

A firm faces the production function Q = 4K0.5 10.5 where K is capital and L is labor. a. Find the first-order partial derivatives, provide an economic interpretation. b. Find the second-order partial derivatives, provide an economic interpretation of the results. c. Find the cross-order partial derivatives, provide an economic interpretation of the results. d. What is the maximum output the firm can produce with a budget of $200 if the price of K is $4 per unit and the price of L is $2 per unit?

Suppose the Sunglasses Hut Company has a profit function given by P(q) = -0.01q² +5q — 42, where q is the number of thousands of pairs of sunglasses sold and produced, and P(q) is the total profit, in thousands of dollars, from selling and producing a pairs of sunglasses. A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) Answer: MP(q) B) How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your answer to three decimal places.) = Answer: pairs of sunglasses need to be sold. thousand C) What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your answer to three decimal places.) thousand Answer: dollars of maximum profits can be expected.