Question 1 A computer retailing company specializes in the sale of jump drives to community colle students. The demand function for jump drives is p=2+10v+1000 dollars For the same company the average cost function is given as T=2x +36v-1600 - dollars Where p is the price m dollars and x represents units of output. 1) Determine the revenue funetion Determine the cost function Determine the profit funetion 11) 111
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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…
- Price and cost (dollars per student) $150 120 88 76 72 ATC 40 - MC MR 24,000 30,000 36,000 Quantity of students enroiled 15,000 Your college decides to offer a psychology course as a MOOC that can be taken by students anywhere in the world, whether they are actually enrolled in your college or not. The demand and cost situation for the MOOC is shown in the figure. The faculty member who designed the course argues: "I think the course should be priced so that the maximum number of students enroll." Which price should this faculty member favor? O A. $0 В. $40 C. $88 D. $1502AAWO AC I4 17.1 REVENUE, COST, AND PROFIT APPLICATIONSITSO RSYHAHD 797 20 A firm sells each unit of a product for $50. The total cost of producing x (thousand) units is described by the function C(x) = 10 – 2.5x² + x³ where C(x) is measured in thousands of dollars. (a) Use the marginal approach to determine the profit-maximizing level of output. (6) What is total revenue at this level of output? Total cost? Total profit? 1 The profit function for a firm is -000Profit Suppose that the total weekly cost for theproduction and sale of x bicycles is C(x) = 23x +3420 dollars and that the total revenue is givenby R(x) = 89x dollars, where x is the number ofbicycles.a. Write the equation of the function that models theweekly profit from the production and sale of xbicycles.b. What is the profit on the production and sale of150 bicycles?c. Write the function that gives the average profit perbicycle.d. What is the average profit per bicycle if 150 areproduced and sold?
- Question Four a) A fim, focusing on producing meat pie has a demand function 20 25-0.25P. If fixed cost is 145 and variable cost per urit function is 2Q- 40 + , where Q is number of meat pie produced and Pis the price per unit: i. 275 Determine the number of meat pies that maximizes the company's profit. ii. How much should the fimcharge per unit of the product? iii. Find the total profit at the profit mximizing level of output. iv. Using the own price edasticity of demand, comment on the fimis pricing policy optiors. b) The production function for Amzonbuưgers, producers of delicious burgers at Sao Tome, is given as: Q = K%L% If the wage rate is $15 per unit of labour, and cost of capital is $1,920 per unit and you have 1 unit of capital which carmot be changed, and the firmemploys 8 units of labour; i. Calculate the fimts total cost ii. Calculate the fim's average cost ii. Estimate the marginal product of labourASK YOUR TEACHER The function gives the weekly profit, in thousand dollars, that an airine makes on its fights from Boston to Washington DC when the ticket price spelers 2nterpret the f () (60)-S When the ticket price is s (b) (60)-4.5 When the ticket price is s () (90)--2 [SA When the ticket price is s the weekly profit to the airline on fights from Boston to Washington is s MY NOTES the weekdy profit to the airtine on fights from Boston to Washington is by the weekly profit to the airine on fights from Bestion to Washington bedby)A two Product finm faces the follow- = 40-2P1 demand and Cost function 8- a) Find the output levels that satiaty the 12 demand amd 40-2P,-P2 タ,=35-P、- 8 follow- ng Cont function8 32 Demand function. C%=8it 20+ 10 cost function. a) Find the output levels that sati. order Conditions ythe tor maximum profit. 6)check the 2nd (ondition. Can you conclude that this Problem Posses a Order for sufficient unique maximum) c)What in the maximal profit?
- The blue curve on the fallowing graph represents the demand curve facing a firm that can set its own prices. Use the graph inout tool to help you answer the folowing questions. You will not be graded on any changes you make to this graph. Note: Once you enter a value in a white fidld, the graph and any corresponding amounts in cach grey field will change accordingly. Graph Input Tool Market for Goods 200 nguantity Semanded 20 100 Demand Price (Dolars per unt) 140 100.00 120 100 Demand 40 20 12 16 20 24 21 2 M 40 QUANTITY Iunita) On the graph inpue tool, change the number found in the Quantity Demanded feld to determine the prices that correspond to the production of 0, 8, 26, 20, 24, 32, and 40 units of output Calculate the total revenue for each of these production leveis. Then, on the fallowing graph, use the green paints (triangie symbal) to plot the resuuts. 2000 Tata Revenue 200 00 400 200 16 20 QUANTITY (Number of uni) 12 24 20 40 Calculate the total revenue if the firm produces…Su Jappose that the profit function tor a com modity X)=-0.01x2+20x-1990 where 3. X13 the number of Acms sold, Find the marginal profit at x=50 and tell what ;it tems so predizds.2500 2000 1500 Returns te scale: 0.33 1000 Price 2 10 15 20 25 30 Size dength in feet) 35 40 Rental price 100 The interactive above is from the loarning object, it will automatically find the profit maximizing length of the truck Adam should rent at given prices, rental rates, productivities, and returns to scale. It only the productivity of the truck Adam chooses to rent decreases, which of the following would be true at the new profit maximizing level of output and length of truck? Select the two that apply O A decrease in marginal cost O A decrease in total costs O A decrease in total revenuo O An incroase in the amount of labor Adam hires Revenue