Given Cost and Price (demand) functions C(q) = 110q + 45000 and p(q) = - 2.8q+ 800, what profit can be earned if the price is set to be $550 per item? T 2 The profit is $ 62.50-2,89 29 (Round to the nearest cent.) of C100 o00 ond it costs A company produces a special new tyne of TY Tho nomnonu h
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- A company produces and sells a consumer product and is able to control the demand for the product by varying the selling price. The approximate relationship between price and demand is p= 200-0.05D where p is the price per unit in dollars and D is the demand per month. The company is seeking to maximize its profit. The fixed cost is $15000 per month and the variable cost is $50 per unit. a. What is the number of units that should be produced and sold each month to maximize profit? b. What is the domain of profitable demand during a month? Show your spreadsheet.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…A firm can produce only 2900 units per month. The monthly total cost is given by C(x) = 400 + 200x dollars, where x is the number produced. If the total revenue is given by R(x) = 350x − 1/100 x2 dollars, how many items, x, should the firm produce for maximum profit? a. x =______ items b. Find the maximum profit.
- 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:) 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?Your product's revenue per unit is $30, and product's cost per unit is $10. If the demand for next month is 200 units, and it costs $1000 one time to set up the machine, what is our profit (in dollars) for next month?
- Give with diagram mandatoryPage of 2 ZO The marginal cost for a manufacturer of cherries is MC(q) = 0.06q° + 0.5g + 50 per necaton-cherry. Find the change in total cost for the manufacturer when production is increased from 40 hecaton-cherries to 50 hecaton-cherries.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.)
- 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 functionect 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 theA 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?
