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 = $ $

sketch a graph of the linear function f(t)= 2t - 5

Amol and Nikhil are both going to Spartan Stadium for the football game. Amol lives 7 miles away and is riding his bike from home towards the stadium 1 at a pace of miles/minute. Nikhil lives 3 miles away along the same route but is walking from home towards the stadium at a rate of 4 24 miles/minute. Assume that they both started their journey at the same time t = 0. a. (4/10) Find two linear functions, A(t) and N(t), that can be used to find the distance that Amol and Nikhil are from the stadium after t minutes. A(t) = N(t) = Part 2/4. 7-1/4t b. (2/10) Find the time is takes for the first person to arrive at the stadium. Part 3/4. 3-1/24t Lowest time: Part 4/4. c. (2/10) How long will they have been traveling when their paths cross? Time of Crossing: d. (2/10) How far are they from the stadium when their paths cross? Distance to the Stadium: M M Σ minutes Σ minutes Σ miles

At time t = 0, a tank contains 100 liters of water. The piecewise - linear graph below shows the rate R(t), in liters per minute, at which water is being pumped into the tank during a 55 minute period. R(1) (20, 30) (35, 30) 30- 20- 10 (0, 10) (55, 0) 10 20 30 40 50 Time (minutes) a). How many liters of water have been pumped into the tank from time t =0 to time t = 55 minutes? Show the work that leads to your answer. (sin t) b). At time t = 10 minutes, water begins draining from the tank at a rate modeled by the function D, where D (t) = 10e 10 liters per minute. Water continues to drain at this rate until time t = 55 minutes. How many liters of water have drained from the tank from time t = 0 to time t = 55 minutes? Set up a definite integral to represent this situation, and use a graphing calculator/desmos to evaluate the definite integral. Round or truncate answer to 3 decimal places. c). How many liters of water in the tank at time t = 55 minutes? Show the work that leads to your…

Suppose that while driving a car, the driver suddenly sees an animal standing in the road. The driver's brain registers the information and sends a signal to the driver's foot to hit the brake. The car travels a distance D, in feet, during this time, where D is a function of the speed r, in miles per hour, of the car when the driver sees 13 the animal. That reaction distance is a linear function given by D(r) = 10+ 5. Complete parts a through c below. a) Find the slope of this line and interpret its meaning in this application. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The slope m is |. For each mile per hour faster that the car travels, it takes feet longer to stop. O B. The slope is not defined. For each mile per hour faster that the car travels, it takes 0 foot longer to stop.

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…

Consider the demand (D) and supply (S) functions D = 14 - P and S = P² + 3P +2. (P is the unit price by dollars.) 1. Find the domain of the function D = D(P) in this context. 2. Find the equilibrium price Pr. What happens if P > P* (explain in this context)? ( 3. Sketch both the demand and supply curves in one coordinate system. Identify the equilibrium point...

The price p​ (in dollars) and the demand x for a particular clock radio are related by the equation x=2000−20p.   ​(A) Express the price p in terms of the demand​ x, and find the domain of this function. ​(B) Find the revenue​ R(x) from the sale of x clock radios. What is the domain of​ R? ​(C) Find the marginal revenue at a production level of 1200 clock radios. ​(D) Interpret R′​(1600​)=−60.00.

Jim's Camera shop sells two high-end cameras, the Sky Eagle and Horizon. The demands and selling prices for these two cameras are as follows. DS = demand for the Sky Eagle PS = selling price of the Sky Eagle DH = demand for the Horizon PH = selling price of the Horizon DS = 228 − 0.60PS + 0.35PH DH = 280 + 0.10PS − 0.64PH The store wishes to determine the selling price that maximizes revenue for these two products. Develop the revenue function R (in terms of  PS  and  PH  only) for these two models, and find the revenue maximizing prices (in dollars). (Round your answers to two decimal places.) Revenue R = 228Ps​−0.60P2s​+0.35Ph​Ps​+280Ph​+0.10Ps​Ph​−0.64P2s​      Price for Sky Eagle PS =$  Price for Horizon PH =$  Optimal revenue R =$