The inverse demand for organic dog food is given by P1 = 24 - 2Q1, and %3D the inverse demand for conventional dog food is given by P2 = 12 - Q2, %3D where P is the price of dog food in USD/lb, and Q is the quantity of dog food in thousand pounds. The cost of producing dog food is C(Q) = 2Q. %3D The profit-maximizing quantity of organic dog food is equal to (1000s): 6 8. 5.5 O 2
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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 function|1.6.1 A company manufactures and sells x dellphones per week. The weekly price-demand and cost equations are given below. p= 400 - 0.5x and C(x) = 20,000 + 140x (A) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? What is the maximum weekly revenue? The company should produce (Round to the nearest cent as needed.) phones each week at a price of $ The maximum weekly revenue is $ (Round to the nearest cent as needed.) (B) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit? What is the maximum weekly profit? The company should produce (Round to the nearest cent as needed.) phones each week at a price of $ The maximum weekly profit is $ (Round to the nearest cent as needed.)BigSwaba Corp produces virus home test kits which it sells in the market. It pays a marketing company to post Instagram images of people using the kits in the comfort of their own homes. The demand for the kits and cost of production are as follows: 1 1 Cost: C=200+=q´ +m 1/2 Demand: p=48+m/: Where m is the firm's marketing expenditure. Assume the CEO of BigSwaba asks you to help the company maximize profit. а. How many kits should the company sell and at what price? b. What is the demand elasticity at this output level? C. What should their marketing budget be? Assume the CEO of BigSwaba realizes her bonus will determined not by profits, but by the firm's revenue. Maintaining the same marketing budget as in part a: d. What quantity should the firm produce to maximize revenue?
- 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…You are the CEO for a lightweight compasses manufacturer. The demandfunction 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.Caustic sodaSuppose that demand for caustic soda in Freedonia is given by D(P) = 10000 - 2P, where the quantity demanded is measured in units per year and the price P is in $ per unit. The market for caustic soda in Freedonia is perfectly competitive and consists of many price-taking firms each operating an identical plant. Caustic soda production requires chlorine which all plants must buy from a monopolist named Freedonia Chlorine Corporation (FCC). FCC can produce chlorine at zero marginal cost and has no fixed costs. Producing one unit of caustic soda requires one unit of chlorine and FCC charges a price of PC per unit of chlorine. Caustic soda plants have constant marginal cost which is MC = $(PC + 1000). (For example, if PC = $200 then each plant has MC = $1200.) Suppose caustic soda firms have no fixed costs and there are no capacity constraints in the market. a. Suppose a new market opportunity opens up and FCC can now sell chlorine in Baldonia as a monopolist. Demand…
- George has been selling 5,000 T-shirts per month for $8.50. When he increased the price to $9.50, he sold only 4,000 T-shirts. Which of the following best approximates the price elasticity of demand? -2 -2.2 -2.6 -1.8 Suppose George's marginal cost is $5 per shirt. Before the price change, George's initial price markup over marginal cost was approximately . George's desired markup is . Since George's initial markup, or actual margin, was than his desired margin, raising the price was .The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Buddies, a purely competitive firm that produces novelty ear buds. Assume the market for novelty ear buds is a competitive market and that the price of ear buds is $6.00 per pair. Quantity of Ear Buds MC ($) ATC ($) 10 - 5.00 15 2.00 4.00 20 2.44 3.61 25 3.56 3.60 30 4.02 3.67 35 5.49 3.93 40 5.93 4.18 45 8.59 4.67 Instructions: In part a, enter your answer as the closest given whole number. In parts b–d, round your answers to two decimal places. a. If Buddies wants to maximize profits, how many pairs of ear buds should it produce each week? _ pairs b. At the profit-maximizing quantity, what is the total cost of producing ear buds? $ _ c. If the market price for ear buds is $6 per pair, and Buddies produces the profit-maximizing quantity of ear buds, what will Buddies profit or loss be per week? $ _ d. Now assume the market price is $5.50 per…Mango Systems believes that demand for its pet e-mouse follows a linear demand equation: Quantity = 43,911 - 708* Price Mango's variable cost to produce one pet e-mouse is $23.50. Find the maximum total contribution margin (margin per unit times quantity sold) that Mango Systems can possibly achieve on its pet e-mouse. (Rounding: penny.) Your Answer:
- A garden shop determines the demand function D(p) = 4p+1000 during early summer for %3D 40p+26 comato plants where q is the number of plants sold per day when the price is p dollars per plant. a. Find the price elasticity of demand equation. b. Calculate the price elasticity of demand at a price of $3. Is the demand elastic, inelastic, or unit elastic? How do you know? C. Based on the information in part b, should the garden shop increase, decrease, or leave the price the same at $3 if it wants to increase revenue? Explain. d. Calculate the revenue before the price change and after to support your answer to part c.A flour mill buys its wheat from two different farms, then processes the wheat into flour. Wheat from Farm X costs the mill $7 per bushel, and wheat from Farm Y costs the mill $15 per bushel. The selling price (in dollars per bushel) for the mill's wheat can be modeled by p(x, y) = 500 x y where x is the demand for the flour milled from Farm X's wheat and y is the demand for flour milled from Farm Y's wheat. Assume that x and y may be zero (so the mill only buys from one of the suppliers) and that the mill can by 1/2 of a bushel. Then the maximum profit is attained when x = y = bushels bushels The amount of the flour mill's maximum profit is $Exercise 5.4 A company is producing and selling branded milk with the following total cost function: CT(q)= 0.2q²+q+70. If the demand function for this brand of milk is: P=15-0.5q: a) Calculate the optimal price of milk, as well as the optimal quantity sold and the profits of the company. b) Calculate the price elasticity of demand in the equilibrium of the company. c) Justify why the company has an excess of productive capacity. d) Represent graphically.