Mary owns a Mrs. Field's cookie shop. The number of cookies sold in a day, x, depends on the price of the cookie, p, and is given by the relationship x = -2000p + 4000. If Mary wants to bring in a daily revenue of $1020, what is the highest price she can sell her cookies at to make $1020?
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Mary owns a Mrs. Field's cookie shop. The number of cookies sold in a day, x, depends on the
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- For a certain company, the cost function for producing x items is C(x)=30x+250 and the revenue function for selling x items is R(x)=−0.5(x−100)2+5,000. The maximum capacity of the company is 140 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. Assuming that the company sells all that it produces, what is the profit function? P(x)= . Hint: Profit = Revenue - Cost as we examined in Discussion 3. What is the domain of P(x)? Hint: Does calculating P(x) make sense when x=−10 or x=1,000? 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 = Profit when producing 80 items =…After an analysis of a large number of small businesses with two to nine employees, it was determined that, in a certain market sector, the operating costs C, in thousands of dollars, could be modeled by the function(pic#2)...., where p is the number of employees working for the firm. On the other hand, the realized revenue, R, of a firm could be determined as a function of the operating costs C, where R=(pic#1)... R and C are expressed in thousands of dollars. a) Based on the analysis, what would be the operating costs for a business with three employees? b) What would be the revenue for a company with three employees? c) Determine the equation that would model the realized revenue, R, as a function of the number of employees.Refer to the figure below to answer the questions. 1.) A corn producer's profit is RM200 and is producing 100 bushels of corn. Then he must have a cost per bushel of __________. 2) A corn producer produces 80 bushels of corn and sells each bushel at RM5. The cost of producing each unit bushel is RM2. This corn producer's total revenue is ________ and profit is ________. 3) A corn producer's total revenue is RM1,000. If she sells each bushel of corn for RM5, she must be selling ________ bushels of corn.
- A firm has production function F(K, L) = 1/4 (K1/2 + L1/2) . The wage rate is w = 1 and the rental rate of capital is r = 3. (a) How much capital and labor should the firm employ to produce y units of output? (b) Hence find the cost of producing y units of output (the firm’s cost function). (c) Differentiate the cost function to find the marginal cost, and verify that it is equal to the value of the Lagrange multiplierLet 10p + x = 100 be the demand equation, where p is the price per item when x items are demanded. (a) Find the total revenue when the level of production is: (i) 40; (ii) 41; (b) Find the exact revenue derived from the 41st item. (c) Find the approximate revenue derived from the 41st item. (d) What is the error if the derivative is used to approximate the marginal revenue?Cost, revenue, and profit are in dollars and x is the number of units. A firm knows that its marginal cost for a product is MC = 2x + 20, that its marginal revenue is MR = 44 − 6x, and that the cost of production of 100 units is $12,160. the optimal level of production is 3 units. a) find the profit function b) Find the profit or loss at the optimal level.
- Suppose that the Travnikar Corporation manufactures widgets. Analysts that work for the company have found a function C(x) which reports the cost to produce x widgets and a function R(x) which reports the total revenue from selling x widgets. Currently, the company is producing 500 widgets, but the analysts find that R'(500)=85 and C'(500)=79. In order to maximize profits, should the analysts recommend increasing or decreasing production?The daily cost to manufacture generic trinkets for gullible tourists is given by the cost function C(x) = −0.001x2 + 0.3x + 500 dollars where x is the number of trinkets. a. As x increases, the marginal cost(A) increases (B) decreases (C) increases, then decreases. (D) decreases, then increases. b. As x increases, the average cost(A) increases (B) decreases (C) increases, then decreases. (D) decreases, then increases. c. The marginal cost is(A) greater than (B) equal to (C) less than the average cost when x = 100.Market research for a certain ice cream company indicates that if the price per cup of ice cream is P50.00, the demand will be 1200 cups, whereas if the price is increased to P60.00, the demand will be 1100 cups. Therefore, at a production level of 200 cups of ice cream, the revenue generated by the company would be $130 for each additional cup of ice cream produced. Now, suppose it is known that the total cost of production of x cups of ice cream is given by C(x) = 3x + 25,500. (a) Find the value(s) of x at the break-even points. (b) Use marginal analysis to approximate the profit from the sale of the 500th cup of ice cream. Compare this value with the exact profit from the sale of the 500th cup.
- Suppose your product sells for $1.20 per unit. The total cost of producing x units is C(x) = 50 + 0.20x + .001x^2 dollars. a.) Find the marginal revenue and marginal profit functions b.) Find the marginal profit when x = 400 c.) What is the approximate profit from selling the 401st unit? d.) Find the value of x for which the marginal profit is zero.The demand and supply for a whole pizza in Mr Hot’s Market are given by the equations, Qd = 6,300 – 530P and Qs = 1,200 + 150P. What is the Statement of the Problem?1. Inputs K, L, R and M cost £10, £6, £15 and £3 respectively per unit. What is the cheapest way of producing an output of 900 units if a firm operates with the production function Q = 20K0.4L0.3R0.2M0.25? 2. Make up your own constrained optimization problem for an objective function with three variables and solve it. 3. A firm faces the production function Q = 50K0.5L0.2R0.25 and is required to produce an output level of 1,913 units. What is the cheapest way of doing this if the per-unit costs of inputs K, L and R are £80, £24 and £45 respectively?
