The manufacturer of smart printers is trying to decide what price to set for its product. The demand and cost function are assumed to be as follows: P = 80 -2Q TC= 160 +50Q-1.5Q ²
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The manufacturer of smart printers is trying to decide what price to set for its product. The
demand and cost function are assumed to be as follows:
P = 80 -2Q
TC= 160 +50Q-1.5Q ²
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Solved in 2 steps
- The Rainwater Brewery produces beer. The annual fixed cost is $150,000, and the variable cost perbarrel is $16. Price is related to demand according to the following linear equation.v -75,000 1,153.8pDevelop the nonlinear profit function for the brewery and determine the price that will max-imize profit, the optimal volume, and the maximum profit per year.The cost, in dollars, of producing x yards of a certain fabric is C(x) = 900 + 12x - 0.1x² +0.0005x³ and the company finds that if it sells x yards, it can charge p(x) = 27-0.00021x dollars per yard for the fabric. (a) Graph the cost and revenue functions. y 8000 6000 4000 2000 y 15 000 10 000 5000 R C 100 R =² C 100 200 200 300 300 X 400 400 X Use the graph to estimate the production level for maximum profit. 283.092 x yards y 15 000 10 000 5000 y 15 000 10 000 5000 R 100 R C 100 200 200 (b) Use calculus to find the production level for maximum profit. (Round your answer to two decimal places.) 186.63 yards 300 300 400 400 XBest Ink Printing Co. received an order to print a minimum of 50,000 tickets for a concert. They have three printing machines available to meet the order they received. The set-up cost of these machines and the unit cost/ticket printed using each machine along with their maximum production are provided in the table below: Machine A B 976400 C Cost per unit $18 $21 $24 Maximum Production 30,000 25,000 30,000 Formulate an all-integer linear programming model to find the required number of tickets produced by each machine in order to minimize the production cost. What is the optimal solution for the number of tickets produced by machine B?
- if the selling price of a certain product is shown in the figure below and the variable cost per unit is 31. then the demand the gi maximum profit is 452units Ob. 470units Oc 455units Od. 450units Oe 445units if the selling price of a certain product is shown in the figure below and the variable cost per unit is 31. then the demand the gives maximum profit is +8D-1X1o D=1600 452units Ob 470units OC 455units Od. 450units 4n45unitsA large wood products company is negotiating a contract to sell plywood overseas. The fixed cost that can be allocated to the production of the plywood is $84309 per month. The variable cost per thousand board feet is $220.0 for demand 2176 units. The price charged will be determined by P-$739-0.07D per 1000 board feet. For this situation, calculate the profit for the mentioned scenario. Select one: a. 1045034.93 O b. 713586.68 C. 3498584082.68 d. 1213500.68You're company manufactures on large scale unit and it has been shown that marginal or variable cost are given by this function (92-2x)sh where xis the number of units of output per annum the fixed costs are 800000 annually, it has also been shown that the marginal revenue which is the gradient ot the total revenue is given by (112-2x) ... required determine by integration the total cost, the total revenue , the break even point of your company and the number of units of output that would maximise total revenue
- 6:08 PM ě 3.5KB/s 1l 82 4G+ 01:52:56 Remaining Multiple Choice If breakeven point is 100 units, each unit sells for P30, and fixed costs are P1,000, then on a graph the: total revenue line and the total cost line will intersect at P3,000 of revenue O total cost line will be zero at zero units sold revenue line will start at P1,000 total revenue line and the total fixed cost line will intersect at P3,000 of revenue 56 of 64 II レThe figure below shows graphs of the fixed cost function, total cost function and the total revenue function for a certain commodity. 20 Dollars (8) 2000+ 7000- 6000 5000 000 3000 2000 1000+ -10 -1000+ 10 20 30 (a) What is the break-even point? e.g. (295,7650) (b) What are the fixed costs? $ TR TC If the selling price per unit is $70, and the variable cost per unit is $30: Percent of capacity= FC 40 50 60 70 80 90 100 Units enter the answer in the form (x,y) (c) If the maximum production capacity of the commodity is 100, express the break- even units as a percent of capacity? % (round to two decimal places if necessary)Answer all parts (a)-(g) of this question.Mette has started Mersea Oysters. She aims to export oysters to Germany where she acts as aprice taker. After a couple of nights of calculations she believes that her cost function is givenby C(q) = 100 + 6q + 2q2, where q denotes kilos of oysters harvested. The market price shewill face in Germany is 50 per kilo.(a) [4 marks] Derive Mette’s marginal cost function.(b) [7 marks] Use your result from (a) to determine the profit-maximizing output level.(c) [7 marks] Explain in words why the supply function for a price taker is the same as themarginal cost function.(d) [8 marks] Calculate Mette’s profit. Illustrate marginal cost and profit in a diagram.(e) [8 marks] Now instead assume that the price is 22. Should Mette produce at this price?(f) [8 marks] Assume again that the price is 22 but that the fixed cost of producing (100) issunk and was taken in the previous period. Should Mette produce at this price in this case?(g) [8 marks] Assume again…
- Answer all parts (a)-(g) of this question.Mette has started Mersea Oysters. She aims to export oysters to Germany where she acts as aprice taker. After a couple of nights of calculations she believes that her cost function is givenby C(q) = 100 + 6q + 2q2, where q denotes kilos of oysters harvested. The market price shewill face in Germany is 50 per kilo.(a) [4 marks] Derive Mette’s marginal cost function.(b) [7 marks] Use your result from (a) to determine the profit-maximizing output level.(c) [7 marks] Explain in words why the supply function for a price taker is the same as themarginal cost function.(d) [8 marks] Calculate Mette’s profit. Illustrate marginal cost and profit in a diagram.(e) [8 marks] Now instead assume that the price is 22. Should Mette produce at this price?(f) [8 marks] Assume again that the price is 22 but that the fixed cost of producing (100) issunk and was taken in the previous period. Should Mette produce at this price in this case?(g) [8 marks] Assume again…(a) A micro-entrepreneur produces caps and hats for women. The output-cost data of the business is reproduced below: Output Total Cost 50 890 100 920 150 1000 200 1260 250 1470 300 1850 350 2410 Using the above data estimate total cost equation and determine the average and marginal cost functions. Dstermine the output rate that will minimize average tost and the peritBavarian Crystal Works designs and produces lead crystal wine decanters for export to international markets. The production manager of Bavarian Crystal Works estimates total and marginal production costs to be aq0 to noiinseu14 Isind TC = 10,000 + 40Q + 0.0025Q² and ivibe to l9v9i ani oi -MC = 40 + 0.005Q1oriism s Arol else noitee eaidT aigie s niged sW noilesimixam benistie iton to laval orfs.ot doagee sideixav, where costs are measured in U.S. dollars and Q is the number of wine decanters pro- duced annually. Because Bavarian Crystal Works is only one of many crystal produc- ers in the world market, it can sell as many of the decanters as it wishes for $70 apiece. Total and marginal revenue are tanad tan ait oT vtivins to briTR = 700 owd io anoilanut ed teoo where revenues are measured in U.S. dollars and Q is annual decanter production. a. What is the optimal level of production of wine decanters? What is the marginal revenue from the last wine decanter sold? and MR = 70 %3D b. What…