The organizer of a sports event estimates that if the event is announced 𝑥 days in advance, the revenueobtained will be 𝑅(𝑥) thousand dollars, where𝑅(𝑥) = 400 + 120𝑥 − 𝑥2The cost of advertising the event for 𝑥 days is 𝐶(𝑥) = 2𝑥2 + 300a. Find the profit function 𝑃(𝑥) = 𝑅(𝑥) − 𝐶(𝑥) and sketch its graph.b. How many days in advance should the event be announced in order to maximize profit? What is themaximum profit?c. What is the ratio of revenue to cost 𝑄(𝑥) = 𝑅(𝑥)𝐶(𝑥) at the optimal announcement time found in part (b)?What happens to this ratio as 𝑥 → 0? Interpret these results

Suppose a granola bar company estimates that its monthly cost is 𝐶(𝑥)=500𝑥2+400𝑥C(x)=500x 2 +400x and its monthly revenue is 𝑅(𝑥)=−0.6𝑥3+800𝑥2−300𝑥+600R(x)=−0.6x 3 +800x 2 −300x+600, where x is in thousands of granola bars sold. The profit is the difference between the revenue and the cost.What is the profit function, P(x)?A.𝑃(𝑥)=−0.6𝑥3+1300𝑥2+100𝑥+600P(x)=−0.6x 3 +1300x 2 +100x+600B.𝑃(𝑥)=0.6𝑥3+300𝑥2−700𝑥+600P(x)=0.6x 3 +300x 2 −700x+600C.𝑃(𝑥)=−0.6𝑥3+300𝑥2−700𝑥+600P(x)=−0.6x 3 +300x 2 −700x+600D.𝑃(𝑥)=0.6𝑥3−300𝑥2+700𝑥−600P(x)=0.6x 3 −300x 2 +700x−600SUBMITarrow_backPREVIOUS

The revenue and cost functions, both in dollars, for the production and sale of x TVs are given as R(x) = 160x − 0.8x2 and C(x) = 3,240 + 15x, respectively.(a)Find the value(s) of x where the graph of R(x) has a horizontal tangent line with correct units. (Enter your answers as a comma-separated list. Round your answers to the nearest integer. If an answer does not exist, enter DNE.)x = 100   (b)Find the profit function in terms of x. (Note: Profit is revenue minus costs.)P(x) = −.8x2+145x−3240 (c)Find the value(s) of x where the graph of P(x) has a horizontal tangent line with correct units. (Enter your answers as a comma-separated list. Round your answers to the nearest integer. If an answer does not exist, enter DNE.)x = 7258​

A firm’s price in a perfectly competitive market is 1000. Its cost function is 32 C(x) = 0.01x 3x− 11+08x 96+0 , where x ≥ 0 is the number of units produced and sold. (a) Find an expression for the profit function π(x) for x ≥ 0. (b) Find all stationary points and determine the profit maximising level of output. answer to six decimal places. 1 √1−𝑥𝑥 . State your answer using (c) Using a sign diagram, determine the intervals over which π(x) is increasing and decreasing. (d) Determine the intervals over which π(x) is concave and convex. (e) Where is the point of inflection in C(x)? Give an economic interpretation of the point of inflection.

Find the breakeven point for the firms with total revenue R(x)=〖-4x〗^2+72x and a cost function of C(x)=16x+180. Sketch the graph to show the breakeven points for the the firms.

Instructions: Use the given information to answer the questions and interpret key features. Use any method of graphing or solving.The roots of the quadratic function describing the relationship between number of products produced and overall profit margin are x=0𝑥=0 and 100100. The vertex is (50,1000)(50,1000).The maximum profit of $$ dollars is reached when items are produced.The first root tells us that the profit will be 00 when products are produced. The second root says once items are made, the company is no longer making any profit. (They do not have production capacity and have to outsource for anything over 5050.)