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- 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. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit 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? Type your answer here:what is coasian transaction cost?Profit 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?
- 1. ThedemandfunctionforagoodisgivenbytheequationP=a−bQwhilethetotalcost function is TC = dQ2 + eQ + f, where a, b, d, e and f are positive constants. (a) Derive the equation for profit.(b) Derive an expression for the value of Q for which profit is maximised.920 it bait of 289301 Sindspis ON SEU pilkupeni A30S AO +32 monulo2 An economist for a sporting goods company estimates the revenue and Cost functions for the production of a new snowboard. These Functions are R(x) = -x ² +10x and ((x) = 4x+5, respectively, where x is the number of Snowboard's produced in thousands. The average profit is defined by the function AP(x) = P(x), where pox) is the profit function & Determine the production levels that make AP(x) > 0 P-xdQuestion Two: The following data for a small farm operating in a perfectly competitive market are given in the table below. The price is $10 per yogurt. Q TC 100 10 200 20 280 30 330 40 360 50 380 60 390 70 425 80 500 90 610 100 750 Instructions: 1. What is the firm's decision at that price? (whether to produce or to shutdown), justify your answer. 2. Show the range of output at which the firm experience IMR and DMR. 3. Using excel, now suppose the price of strawberry yoghurt decreases to $5.5 per unit, what is the right decision firm should take, (produce or shutdown) justify your answer.
- ect of the utility commission's ruling on the profitability of the firm? 15 A company estimates that the demand for its product fluctuates with the price it charges. The demand function is q = 280,000 – 400p where q equals the number of units demanded and p equals the price in dollars. The total cost of producing q units of the product is estimated by the function C = 350,000 + 300q + 0.0015q? (a) Determine how many units q should be produçed in order to maximize annual profit. (b) What price should be charged? (c) What is the annual profit expected to equal? 16 Solve the previous exercise, using the) A 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. Find a function for the average cost of this company. (c) If production increases continuously, what is likely to be the average cost per sink? (d) How many laundry sinks will the company need to produce in order to maximise it′s profits? (e) What is the maximum profit?A firm's production function is given by Q = 40K0.8L0.2 Each unit of capital costs $40 and each unit of labour costs $80. (a) Find the maximum level of output if the total input costs are $400,000. (b) Estimate the increase in production if an addtional $5,000 is made available. (c) Show that the ratio of marginal product to price is the same for both inputs. (a) Maximum output Q = (Round to the nearest integer as needed.) (b) Increase in output is units (Round to the nearest unit as needed.) (c) The ratio of the marginal product of capital to price is (Round your answer to two decimal places.) The ratio of the marginal product of labour to price is (Round your answer to two decimal places.)
- A firm produces bread (B). The company wants to lease new equipment. Themarket offers new high-speed ovens (H) and slower ovens (S) with an oldertechnology. The high-speed ovens can produce twice as much bread in the sameamount time.a) Derive the production function.b) The high-speed ovens cost 100 Euros per month and the slower ovens costs 70Euros per month. In which type of ovens should the company invest?c) If the price of the high-speed ovens remains unchanged, calculate the price of theslow-ovens, at which the company could be indifferent in leasing only high-speedovens, slow-ovens or possibly a combination of both.Drives Co. sells portable hard drives. They can sell 600 drives when the price is $75/drive, and they can sell 720 drives when the price is $45/drive. If x represents the number of drives sold, determine the following. (a) What is Drive Co.'s revenue function? R(x) =_ (b)What is the price per drive (in dollars) when revenue is maximized? _ (c) What is the maximum profit (in dollars) made from the sale of these drives if Drive Co. incurs production costs of $165 per drive and has fixed costs of $625? $_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.