2. If the demand function for products A and B is in the order Pa = 36 - 3Qa and Pb = 40 - 5Qb and the common cost function is TC = Qa' + 2QaQb + 3Q6². With the above information, then calculate: a. Production values A and B at the maximum or minimum profit levels. b. The maximum or minimum profit value c. Did the profit reach its maximum or minimum value? Prove it
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A: C=3Q2+30QP=10Q-13Q2+500QNow,TC=3Q2+30QMC=∂TC∂QMC=6Q+30Now,TR=P×QTR=(10Q-13Q2+500Q)QTR=10Q2-13Q3+500F…
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A: We are going to use single variable profit maximisation method to answer this question.
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- A 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…Revenue and Cost The total revenue function for LED TVs is given by R = 1050x dollars, and the total cost function for the TVs isC = 10,000 + 30x + x2dollars, where x is thenumber of TVs that are produced and sold.a. Which function is quadratic, and which is linear? b. Form the profit function for the TVs from thesetwo functions.c. Is the profit function a linear function, a quadraticfunction, or neither of these?) 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?
- 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 = XOn the graph input tool, change the number found in the Quantity Demanded field to determine the prices that correspond to the production of 0, 6, 12, 15, 18, 24, and 30 units of output. Calculate the total revenue for each of these production levels. Then, on the following graph, use the green points (triangle symbol) to plot the results. Calculate the total revenue if the firm produces 6 versus 5 units. Then, calculate the marginal revenue of the sixth unit produced. The marginal revenue of the sixth unit produced is________. Calculate the total revenue if the firm produces 12 versus 11 units. Then, calculate the marginal revenue of the 12th unit produced. The marginal revenue of the 12th unit produced is_________.Revenue and Cost The total weekly revenue functionfor a certain digital camera is given by R = 550xdollars, and the total weekly cost function for thecameras is C = 10,000 + 30x + x2dollars, where xis the number of cameras that are produced and sold.a. Find the profit function.b. Find the number of cameras that gives maximumprofit.c. Find the maximum possible profit.
- A company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500 per day when producing 15 sinks. The company has a daily demand function of q = 360 − p, where q is the number if laundry sinks demanded and p is te price of a laundry sink. (d) How many laundry sinks will the company need to produce in order to maximise it′s profits?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 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?
- 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.(a) How much is total fixed cost? (b) At what output is the price elasticity of demand equal to -1? (c) At what outputs does the firm break even?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)