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 = $ $

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?

A devastating freeze in California’s Central Valley in January 2007 wiped out approximately 75% of the state’s citrus crop. It turns out that the cost for a box of oranges is a function of the percentage of the citrus crop that was frozen, i.e. LaTeX: c=g\left(P\right) , where LaTeX: c is the price of a box of oranges and LaTeX: P is the percentage of the citrus crop that was frozen. When only 20% of the crop was frozen, the price for a box of oranges was $11.58. However, the price per box was $25.32 when 80% of the crop was frozen. Identify the input quantity of the function. Identify the output quantity of the function. Using the method demonstrated in the Module 3 presentation, create a formula for a linear function that represents this situation. i.e. your formula should use one of the given reference points rather than the vertical intercept. (Note: You will need to first find the constant rate of change.) Re-write your formula in LaTeX: y=mx+b form. Show your work. Identify…

The marginal profit in souls that Freddy Krueger makes from haunting nightmares, x, can be modeled by dP dx = 8x + 20 Find the profit function P if from 2 nightmares, Freddy harvested 60 souls.

A portfolio has a value P(E, S), so that the value P is a function of E, the price of a Euro in Canadian dollars, and S, the level of the TSX stock index. Presently the portfolio is worth $390,000, while a Euro is $1.50 Canadian, and the index is S = 18,000. If the partial derivatives of P have values = 70,000, and = -17, what approximately will the portfolio value be if the price of a Euro goes down by 0.06 and the stock index goes down by 397?

The temperature of the air in Boise is given by the function f(t,h) = 0.01ht² - 0.12ht - 0.6h t² + 12t + 60 Where f is the temperature in degrees Fahrenheit, t is measured in hours (with t = 0 corresponding to 9 a.m.), and h is the height above sea level, measured in thousands of feet. Find all four second order partial derivatives: a. ft(t,h) = b. fth(t,h) = c. fht(t,h) = d. fnn(t,h) =

Find the number of units, x, that produces the maximum profit P, if C(x) = 45+4x and p = 60 - 2x. A. 14 units B. 4 units C. 56 units D. 16 units

The demand for a car wash is  x = 600 − 20p,  where the current price is $5. Find the price elasticity of demand ? for this price. ? =