PQ7.2(a) Case: Average Revenue Demand Curve (AR): P=120 -0.02Q Weekly Production (Q) Price (P) (Cents/Unit) Cost Function (C) = 60Q +25,000 Marginal Cost (MC) = Slope of Total Cost (TC) Curve = 60 Assume: Maximum Profit. Question: What is the Level of Production, Price, and Total Profit per week - assuming Maximum Profit?
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- Given Cost and Price (demand) functions C(q) = 110q + 45000 and p(q) = - 2.8q + 800, what profit can be earned if the price is set to be $550 per item? U The profit is $ 1,?9 (Round to the nearest cent.) A company produces a special new type of TV. The company has fixed costs of $499,000, and it costs STT00 to produce each TV. The company projects that if it charges a price of $2300 for the TV, it will be able to sell 850 TVs. If the company wants to sell 900 TVs, however, it must lower the price to $2000. Assumo a linear demand. What is the marginal profit if 200 TVs are produced It is $ 0 per item. (Round answer to nearest dollar.)14.The demand function for a new product is p(x) = - 2x + 7 , where p is the selling price of the product and x is the number sold in thousands. The cost function is C(x) = x + 2 . a) Determine an equation for the profit, in standard form and in function notation. b) How many units must be sold for the company to break even?A local company is planning to manufacture and market a four-slice toaster. For this toaster, the research department’s estimates are aweekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a price of $20. The financial department’s estimates are fixed weekly costs of$5,000 and variable costs of $5 per toaster. a) Assume that the relationship between price ? and demand ? is linear. Use the research department’s estimates to express ? as a function of ? and determine the domain of the function. b) Using your knowledge from Finite Math, determine the Revenue function in terms of ?. c) Determine the Marginal Revenue at 2 different production levels for example 250 and 500 units. Interpret these results. (HINT: Consider what a positive or negative first derivative implies) d) Assume that the cost function is linear. Use the financial department’s estimates to express the cost function interms of ?. e) Determinethe Marginal costand interpret the…
- Q3) the demand function and total cost function for a product are 6P = 660 − 3Q, TC = 80 − 20Q2 + 600Q (a) Write down expressions for: (i) Average cost, (ii) marginal cost, (iii) total revenue, (iv) Marginal revenue, (v) Profit. (b) Determine the values of Q for which total cost is a maximum. Calculate the maximum costs. Calculate the profit when total costs are a maximum. (c) Determine the value of Q for which profit is a minimum. What is the minimum profit?Given Cost and Revenue functions C(q)=q^3-11q^2+55q+5000 and R(q)=−3q^2+2400q, what cost is incurred when marginal profit is $0? The costs are $________. (Round to nearest cent.) Given Cost and Price (demand) functions C(q)=110q+45000 and p(q)=−2.8q+950, what profit can be earned if the price is set to be $500 per item? The profit is $_______. (Round to the nearest cent.) A company produces a special new type of TV. The company has fixed costs of $465,000, and it costs $1200 to produce each TV. The company projects that if it charges a price of $2300 for the TV, it will be able to sell 750 TVs. If the company wants to sell 800 TVs, however, it must lower the price to $2000. Assume a linear demand. What is the marginal profit if 250 TVs are produced It is $_______ per item. (Round answer to nearest dollar.) A hotel rents rooms to customers by the night. The hotel determines that if it sets the price of the room to be $160 per night, 150 rooms will be rented. In…At its best possible output level, a firm has total revenue of Rs. 7000 per day and total cost of Rs. 14000 per day. What should this firm do in the short run if: 10 (Hint: See normal and abnormal loss) The firm has total fixed cost of Rs. 6000 per day? The firm has total variable cost of Rs. 6000 per day?
- 9 = √KE C10K+5E K = 1 C(q) = 10 +5q² Market price (P) : = 30 = 30 = 10q q = 3 P = MC = Profit per unit π = = = R TC P q q զ π = (P - ATC)q - P 30 25 20 15- - ATC 10 0 p = 30 Cost Curves for C(q)=10+5q² MC Profit ATC AVC AFC о 3 4 5 62. A company produces and sells a consumer product and is able to control the demand for the product by varying the selling price. The approximate relationship between price and demand is 2,700 5,000 p = $38 + D for D >1 D2 where p is the price per unit in dollars and D is the demand per month. The company is seeking to maximize its profit. The fixed cost is $1,000 per month and the variable cost (c,) is $40 per unit. a. What is the number of units that should be produced and sold each month to maximize profit? b. Show that your answer to Part (a) maximizes profit.Crawford Computing finds that its weekly profit, in dollars, from its production and sale of x laptop computers is P(x)=-.002x^3-.15x^2+400x-800 Currently, Crawford builds and sells 9 laptops weekly. (a) what is the current weekly profit? (b) how much profit would be lost if production and sales dropped to 8 laptops weekly? (c) what is the marginal profit with x=9? (d) use answers from parts (a) and (c) to estimate the profit resulting from the production and sale of 10 laptops weekly.
- (b) The total revenue curve of a firm is R(q) = 40q – 12q² and its q- 12.85q + 20 + 30 400 where q is the firm's output. average cost A(q) Derive an expression C(q) for the firm's total cost function. Derive an expression II(q) for the firm's profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firm's profit is maximize v. What is the firms's maximum profit? i. ii.The figure shows graphs of the total cost function and the total revenue function for a commodity. (Assume cost and revenue are measured in dollars.) y 500 400 300 200 100 MR 10 (a) Label each function correctly. function A ---Select--- function B ---Select--- (x, y): = 20 (b) Determine the fixed costs. $ 30 (c) Locate the break-even point. -([ = 40 50 Determine the number of units sold to break even. units A B 60 (d) Estimate the marginal cost MC and marginal revenue MR. MC = X15 Suppose a company has fixed costs of $2100 and variable costs per unit of x + 1500 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 16 1600 1/64 (a) Find the break-even points. (Enter your answers as a comma-separated list.) -x dollars per unit. X = (b) Find the maximum revenue. $ (c) Form the profit function P(x) from the cost and revenue functions. P(x) = Find the maximum profit. $ (d) What price will maximize the profit? (Round your answer to the nearest cent.) $