A firm's marginal revenue function is MR = −9Q + 126. Use indefinite integrals to solve for the total revenue function. What increase in the total revenue will be brought about by selling four additional units if two units are currently sold?
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- Break-Even The total revenue function for Frenchdoor refrigerators is given by R = 550x dollars, andthe total cost function for this same product is givenby C = 10,000 + 30x + x2, where C is measured indollars. For both functions, the input x is the numberof refrigerators produced and sold.a. Form the profit function for the refrigerators fromthe two given functions. b. What is the profit when 18 refrigerators areproduced and sold?c. What is the profit when 32 refrigerators areproduced and sold?d. How many refrigerators must be sold to breakeven on this product?A local newspaper currently has 84,000 subscribers at a quarterly charge of $30.Market research has suggested that if the owners raise the price to $32, they wouldlose 5,000 subscribers. Assuming that subscriptions are linearly related to theprice, what price should the newspaper charge for a quarterly subscription tomaximize their revenue?a) Find the cost function (Hint: find slope and use point-slope form to find thecost function) b) Find the revenue function c) Find the maximum revenue d) Find the profit functionA 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…
- Suppose the marginal cost and marginal revenue (in ¢000) for a product produced by a company is estimated to beMC=q+35 MR=560+22q−q2Where q is the quantity produced and the firm’s break-even is 5 units per weekYou are Required to1. determine the total cost and the total revenue function in terms of q.2. estimate the output at which profit is maximize3. calculate the maximum profitA company manufacturing laundry sinks has fixed costs of $100 per day but has totalcosts of $2,500 per day when producing 15 sinks. The company has a daily demand functionof q = 360 − p, where q is the number if laundry sinks demanded and p is te price ofa laundry sink. ) If production increases continuously, what is likely to be the average cost per sink? How many laundry sinks will the company need to produce in order to maximise it′s profits? What is the maximum profit?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 = X
- A manufacturer of electric switches in a competitive industry has a fixedmonthly cost of $50,000, total monthly variable cost $100,000, and marginalcost of $5. What is the profit if the monthly production is 100,000 units?Assuming that prices of switches fluctuate from month to month, what is the lowest price the manufacturer can accept in order to stay in business in the long run and in the short run. Will those prices be the same? Show detail work(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p 40 – 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (1) Write an equation giving profit as a function of the number of lightweight compasses produced. (11) At the moment the company produces 2 million lightweight compasses and makes a pre of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Σ BIUG G |卡 三 = 9 ..Consider total cost and total revenue given in the following table: TABLE IN IMAGE Calculate profit for each quantity. How much should the firm produce to maximize profit?(ii) Calculate marginal revenue and marginal cost for each quantity. Graph them. (Hint: Put the points betweenwhole numbers. For example, the marginal cost between 2 and 3 should be graphed at 2½.) At what quantitydo these curves cross? How does this relate to your answer to part (a)?(iii) Can you tell whether this firm is in a competitive industry? If so, can you tell whether the industry is in along-run equilibrium? (8.75)
- Bessie wants to calculate the accounting and economic profits on her cattle farm in Nebraska. She pays $130,000 per year as her explicit costs for the cost of raising cattle, wages, and insurance. She forgoes $30,000 per year that she could make as a teacher. If her total revenue equals $140,000, that means her accounting profit is and her economic profit is a) $60,000; $30,000 b) $30,000; -$30,000 Oc) -$10,000; -$10,000 d) $10,000; -$20,000Jasmine decides to make and sell jelly cups. It costs jasmine Rs.1000 to set up and Rs.50 per cup made. She decides to sell each cup for 150. By using this information, answer the following questions: A) Write and equation for jasmine's revenue, cost and profit functions? B) Graph each function on a set of axes? C) Find the breakeven point from these graphs? ( D) How many jelly cups will jasmine need to sell in order to make a profit? (E) If jasmine wishes to make a profit of 50, how many jelly cups does she need to sell?Consider the following demand function P = 62 - 2Q and the Cost for the business is $150 (for initial capital required) plus $2 for each item made. (i) Determine the equation for the profit and find the optimum value. (ii) Is the profit increasing or decreasing on approach to the optimal value from the left? 000.05 mu em 10 (iii) Is the rate of change in the profit change itself (marginal rate) increasing or decreasing? (iv) Investigate the approach to the optimal value from the right.
