For a certain company, the cost function for producing items is C (x) = 30 x + 150 and the revenue function for selling æ items is R(x) = -0.5(x - 100)2 +5,000. The maximum capacity of the company is 160 items. The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C (x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit! Answers to some of the questions are given below so that you can check your work. 1. Assuming that the company sells all that it produces, what is the profit function? P(x) = Hint: Profit = Revenue - Cost as we exam ned in Discussion 3. 2. What is the domain of P(x)? Hint: Does calculating P(x) make sense when x = -10 or = 1,000? 3. The company can choose to produce either 70 or 80 items. What is their profit for each case, and which level of production should they choose? Profit when producing 70 items = Number Profit when producing 80 items = Number 4. Can you explain, from our model, why the company makes less profit when producing 10 more units?

Find the marginal cost, marginal revenue, and marginal profit functions. C(x) = 7x²; R(x) = x³ + 11x + 15 marginal cost marginal revenue marginal profit Find all values of x for which the marginal profit is zero. Interpret your answer. (Enter your answers as a comma-separated list.) X =

The company AffordableStuff sells cell phones. The marginal cost for each cell phone is given by the equation C(x) = 0.01x² – 3x + 229. a is the number of cell phones manufactured and sold. The marginal revenue function is R(x) = 429 – 2.x. Both C(x) and R(x) are given in dollars. a) Where do these curves intersect? What do those intersection points mean? b) Find the area between the curves, using end points that make sense. Round to the nearest cent. c) What does the area under the curve mean in this case?

Total profit is defined as total revenue, R(x), minus total cost, C(x), and is given by the function P(x)=R(x)-C(x). Given R(x)=59x-0.4x^(2) and C(x)=2x+15, find each of the ollowing. P(x) R(80),C(80), and P(80)

p=D(x)=71.5−0.02xp=D(x)=71.5−0.02x dollars. The total cost for these coffee makers is given by C(x)=0.05x2+5.5x+6200C(x)=0.05x2+5.5x+6200 dollars. Determine the marginal profit for 118 coffee makers.

If the marginal revenue in dollars per unit for a month is given by MR= −0.04x + 36, find the total revenue function provided that R(0)= 25

If C(x) = 19,000 + 400x – 3.6x2 + 0.004x³ is the cost function and p(x) = 1,600 – 9x is the demand function, find the production level (in units) that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.) units Need Help? Read It

A company’s demand and cost functions are given by p(q)=-0.05q+525andC(q)=q3 -7q2 +85q. What price should be set if marginal profit is $0 per item?

A farm produces rice, which is sold in 50 kilogram bags. Let Q denote the number of bagsproduced per week during harvest time. Costs C are denoted in units of dollars. The totalweekly cost function for producing the product is C = 4Q + 100. The total weekly income function for this product is I = 50Q – 2Q2. What is the profit function P as a function of Q and sketch it using P values 0, 5, 10,15, 20 and 25.

A firm faces the following average revenue (demand) curve: P = 100 - 0.01Q where Q is weekly production and P is price, measured in cents per unit. The firm's cost function is given by C = 50Q + 30,000. Assuming the firm maximizes profits, the firm's level of production is price in cents is and total profit per week in dollars is (please put your answer for price, quantity and profit in numerical values without any dollar sign, comma or decimal place). If the government decides to levy a tax of 10 cents per unit on this product, the new level of production is the price received by the monopolists after tax in cents is and total profit per week in dollars is the price facing the consumer after the imposition of the tax in cents is (please put your answer for price, quantity and profit in numerical values without any dollar sign, comma or decimal place).