1. Verify numerically that when TC = Q² mar- ginal cost is MC = 2Q. 2. What are the optimal output, price, and profits can select the quantity to purchase. What transfer price will the manufacturing unit select? What are the resulting profits of the %3D %3D for the firm? two units? 4. From the firm's standpoint, what is the optimal transfer price? 3. Now assume that the firm is divided into two profit centers. One division manufactures the

1. Verify numerically that when TC = Q² mar- ginal cost is MC = 2Q. 2. What are the optimal output, price, and profits can select the quantity to purchase. What transfer price will the manufacturing unit select? What are the resulting profits of the %3D %3D for the firm? two units? 4. From the firm's standpoint, what is the optimal transfer price? 3. Now assume that the firm is divided into two profit centers. One division manufactures the

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter5: Investment Decisions: Look Ahead And Reason Back

Section: Chapter Questions

Problem 7MC

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Sampson Ltd produces two products that can be produced on either of two machines. Each month, only 5o0 hours of time are available on each machine. The time required to produce each item by hour and machine is: Machine Machine Product 1 Product 2 3 4 Month Month 1 Month 2 Month 1 Demand Demand Price Price Product 1 100 160 $45 $65 $10 Product 2 120 110 $35 The demand and price point for each product that customers are willing to pay are above. The company goal is to maximize revenue from sales from the next two months. Based on the provided information, how many constraints does this problem have excluding the non-negativity constraints?
show solution An oil refinery produces one base type of crude oil. The total cost is given by the equation Total Cost, TC = 50,000+20.2D +0.0001D2. The sales price in dollars per barrel is 35. At what level of production in barrels/week is cost/barrel minimum? What is the minimum cost per barrel? What is the maximum weekly profit that the company can make? At what level of production is the maximum weekly profit attainable? and Over what range of production is profit possible? Express answers in whole numbers and write the numerical values only.
A toy manufacturer makes miniature trucks. The pricep(in dollar) and the demandx(numberof miniature trucks) are related by the equation 6000−600p=x. The total cost for the sametoy manufacturer to producexminiature trucks can be modeled byC(x) = 8x+ 450.(a) (10 points) Express the pricepin terms of the demandx. Find the revenueR(x) if themanufacturer sellsxminiature trucks in a month and find the domain of this function.(b) (10 points) Graph the cost and revenue functions on the same coordinate system for 0≤x≤6000.(c) (10 points) What is the minimum number of trucks the toy manufacturer must sell tobreak even?(d) (10 points) FindP′(300) and interpret the result.(e) (10 points) What is the exact profit from the sale of the 301stminiature truck?
1. A large wood products company is negotiating a contract to sell plywood overseas. The fixed cost that can be allocated to the production of plywood is $600,000 per month. The variable cost per thousand board feet is $125.50. The price charged will be determined byp = $550 – (0.4)D per 1.00 board feet. a. For this situation, determine the optimal monthly sales volume for this product and calculate the profit (or loss) at the optimal volume. b. What is the domain of profitable demand during a month?
A company estimates that the relationship between. unit price and demand per month for a potential new product is approximated by p= $100.00-$0.10D. The company can produce the product by increasing fixed costs $17,500 per month, and the estimated variable cost is $40.00 per unit. What is the demand that maximizes revenue and the maximum revenue? What is the optimal demand, D*, and based on this demand, should the company produce the new product? Why? (Work out the complete solution by differential calculus, starting with the formula for profit or loss per month.)
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
Maximize profit 4D + 3WWith constraintsTime 3D + 2W ≤ 150Cost 2D + 4W ≤ 220D, W ≥ 0 We saw the best point was (20, 45) with profit 215. Use this problem and the notes to answer the following (except part 4):1 write true or false and then explain either response to this – the range of optimality on the D variable refers to how much the value 20 in the best point can go down or go up and this point is still the best,2 write true or false and the explain either response to this – the range of feasibility of the time constraint refers to the value 150 and how much if can change and the best point is still (20, 45),3 write true or false and explain either response to this – the shadow price of .125 on the cost constraint means that if the right hand side of the constraint (the 220) is anywhere between 100 and 300 then each 1 unit increase in this RHS (say from 100 to 101) will increase profit by 12.5 cents and any 1 unit decrease in this RHS will decrease profit 12.5 cents,4 write true or…
4. Optimize the following function and comment about the findings. y =-5x; +10x, + x,x, - 2x{ +4x; +2x,x, - 4x 7. Minimize the cost of 434 units of production for a firm whenQ = 10K'L and P, = 28, P.=10 by finding the critical values and using the bordered Hessian to satisty the 1" order necessary and 2 order suficient condition.
Each time a song is played on the radio, the record company and the songwriter are paid a royalty of $0.30.Of the total, 75% goes to the company and the rest to the writer. If on a network of 50 radio stations, a certainsong is played 4 times a day during the first week and then 20 times a day for the next three weeks, how muchdoes the network owe in royalties for the four weeks? How much do the record company and the songwriterreceive each
Question 3 to the cost of producing the (x + 1)st item? a Can you think of a cost function, so that the marginal cost at any r is exactly equal If yes, describe as many such functions as possible. If not, show why such a function cannot exist. Type here to search 7:00 PM ENG 4/27/2021 Esc Lock F1 F2 F6 F3 F4 F5 F7 Home End Delete F8 F9 F10 F11 F12 Insert %23 $4 & * 7. 4 5 6 Backspace 80 W E R T Y U S D F G H J K L B N M Alt Alt PrtSc Ctrl PgUp
Problem 1. During your first month as an employee at Greenfield Industries (a large drill-bitmanufacturer), you are asked to evaluate alternatives for producing a newly designed drill bit on aturning machine. Your boss’ memorandum to you has practically no information about what thealternatives are and what criteria should be used. The same task was posed to a previous employeewho could not finish the analysis, but she has given you the following information: An old turningmachine valued at $350,000 exists (in the warehouse) that can be modified for the new drill bit.The in-house technicians have given an estimate of $40,000 to modify this machine, and they assureyou that they will have the machine ready before the projected start date (although they havenever done any modifications of this type). It is hoped that the old turning machine will be able tomeet production requirements at full capacity. An outside company, McDonald Inc., made themachine seven years ago and can easily do the…