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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?The cost, in millions of dollars, of building a three-story high school in NewYork State was estimated to be: 2C x x x x 1.7 0.14 0.0001 20 400where x is the number of thousands of square feet. Suppose that you arecontemplating building a for-profit three-story high school and estimate thatyour total revenue will be $0.2 million dollars per thousand square feet.(a) What is minimum area for a three-story high school in New YorkState, that this model covers? (b) What is the variable cost of building a three-story high school in NewYork State? (c) What is the fixed cost of building a three-story high school in NewYork State? (d) Determine the profit function,P x( ), for building a three-story highschool in New York State? . (e) Determine,P(250) , for building a three-story high school in New YorkState, and interpret the result. (f) How many thousands of square feet should a three-story high schoolbuilding in New York State be in order to break even?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. ) 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?
- The world price of zinc has increased to the point where “mothballed” zinc mines in east Tennessee have been reopened because of their potential profitability. (a) What is the estimated annual profit for a mine producing 20,000 tons per year (which is at 100% capacity) when zinc sells for $1.00 per pound? There are variable costs of $20 million at 100% capacity and fixed costs of $17 million per year. (b) If production is only 17,000 tons per year, will the mine be profitable?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…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.
- A,B and C are SOLVED (3) 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.(a) If we assume that the total cost per day is linearly related to the amount of sinksproduced in a day, derive the total cost function of the company?(b) 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?Suppose a company has fixed costs of $300 and variable costs of 3/4 x+1460 dollars per unit, where x is thetotal number of units produced. Suppose further that the selling price of its product is 1500−1/4 x dollars per unit.(a) Find the break-even points.(b) Find the maximum revenue.(c) Form the profit function from the cost and revenue functions and find maximum profit.(d) What price will maximize the profit?A 62 metre length of rope is cut into pieces whose lengths are in arithmetic progressionwitha common difference of d metres. Given that the lengths of the shortest and thelongest pieces are 0.5 and 3.5 metres respectively, find d.(C) For a firm’s product, the demand function isp = 72 2 0.04qand the average cost function isc¯ =500q+ 30 At what level of output would profit be maximized?
- 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?Only typed answer and don't use chat gpt and please answer correctly Suppose that you can sell as much of a product (in integer units) as you like at $61 per unit. Your marginal cost (MC) for producing the qth unit is given by: MC=9q This means that each unit costs more to produce than the previous one (e.g., the first unit costs 9*1, the second unit (by itself) costs 9*2, etc.). If fixed costs are $50, what is the optimal output level? Please specify your answer as an integer. Also, assume that a competitive firm has the total cost function: TC = 1q3 - 40q2 + 710q + 1700 Suppose the price of the firm's output (sold in integer units) is $550 per unit. Using tables (but not calculus) to find a solution, what is the total profit at the optimal output level? Please specify your answer as an integer.This is a repeated question since you guys only answerone question at a time! Let's assume that a firm's total weekly costs are as follows: 1. Salaries = $2,600. 2. Supplies = $400. 3. Rent = $800.In addition, the owners have invested their own money into the business. This could have earned them interest of $150 per week if they had chosen to put it into a bank instead of investing it into their business. If the firm has weekly revenue of $4,000, what are the firm's accounting profit and economic profit? Show your work please.