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- 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 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 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?
- 2. A refrigerator manufacturer is planning capacity expansions. They have determined that their capacity cost follows the equation below, where f(y) = kya, is the cost of a plant that can produce y units annually. f(y) = 0.0107y⁰.62 They have determined that when a = 0.62, using a = u/(e" - 1) gives a value u = 0.89. Their demand for refrigerators is growing at a rate of 5000 units annually, and they use a 16% interest rate for discounting. At the optimal capacity addition level, what does each capacity installation cost?1. Consider the perfectly competitive market for guitar tuners. The mar- ket price for a guitar tuner is $20 and the cost functions are: TC (q) = .01q² + .2q + 4950 %3D MC (q) = .02g +.2 (a) Find the profit-maximizing quantity of guitar tuners produced by a firm in this market. (b) Calculate the profit each firm will earn in this market (c) Graphically depict the firm's profit-maximization problem. (note: this doesn't need to be to scale but should accurately reflect the sign of the profit) (d) Will firms enter into this market in the long run? (e) Graphically show how the price will change as the market pro- gresses towards a long-run equilibrium. (There's no need to find the exact long-run equilibrium price. Just follow similar steps to what we did in class)Define Q to be the level of output produced and sold, and assume that the firm’s cost function is given by the relationshipTC = 20 + 5Q + Q2Furthermore, assume that the demand for the output of the firm is a function of price P given by the relationshipQ = 25 - Pa. Define total profit as the difference between total revenue and total cost, and express in terms of Q the total profit function for the firm. (Note: Total revenue equals price per unit times the number of units sold.)b. Determine the output level where total profits are maximized.
- (b) You are the CEO for a lightweight compasses manufacturer. The demand 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?1. Teddy J is a manufacturer of dish washing liquid . If his monthly demand function for 750ml size is: q = 4000 − 250p and his total cost function is: C(q) = 500 + 0.2q (i) Derive an expression, R(q) for Teddy J′s total revenue curve.(ii) Derive an expression, Π(q) for Teddy J's profit function.(iii) Determine whether Teddy J′s profit is increasing or decreasing when he produces 5 hundred, 750ml bottles of dish washing liquid.Given cost and price (demand) functions C(q) = 100q + 41,000 and p(q) = - 2q + 890, what price maximizes revenue? My Co It would be $ per item. Cours (Round answer to two decimal places.) Anno Calen Cull
- A profit-maximising firm in a competitive market is currently producing 1,000units of output. It has average revenue of $50, average total cost of $40 and fixed cost of $10,000.a) What is its profit?b) What is its marginal cost?c) What is its average variable cost? Is the efficient scale of the firm more than, less than or exactly 1,000 units?(a) Teddy Jis a manufacturer of dish washing liquid. If his monthly demand function for 750ml size is q = 4000 – 250p and his total cost function is C(q) = 500 + 0.2q. (1) Derive an expression, R(q) for Teddy J's total revenue curve. (ii) Derive an expression, I(q) for Teddy J's profit function. (iii) Determine whether Teddy J's profit is increasing or decreasing when he produces 5 hundred, 750ml bottles of dish washing liquid.nou Given cost and price (demand) functions C(g) = 110g + 43,000 and p(g) = - 1.8q + 890, what price maximizes revenue? len It would be $ per item. (Round answer to two decimal places.) llab lome Quiz Grade Study Goody