Suppose an​ ocean-front hotel rents rooms. In the​ winter, demand​ is:   P1=50−1Q1   with marginal revenue​ of: MR1=50−2Q1.   ​However, in the​ summer, demand​ is: P2=140−1Q2 with marginal revenue​ of:: MR2=140−2Q2.   ​Furthermore, suppose the​ hotel's marginal cost of providing rooms is MC=5+1​Q, which is increasing in Q due to capacity constraints. Suppose the hotel engages in​ peak-load pricing. During the​ winter, the​ profit-maximizing price is  ​$______and the​ profit-maxizing quantity is______rooms.  ​(Enter numeric responses rounded to two decimal​ places.)

The cost, in dollars, to produce x designer dog leashes is C(x) R(x) 7x + 10, and the revenue function, in dollars, is - 3x? + 55x - Find the profit function. P(x) = -322 + 48x – 10 Find the number of leashes which need to be sold to maximize the profit. 8. Select an answer Find the maximum profit. 182 Select an answer > Find the price to charge per leash to maximize profit. Select an answer > V Select an answer What would be the be much for a leash? dogs too much money for a lea leashes dollars

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Suppose that the finance department of our favorite company, TVZ R US, determines that the total = 500+ 2x. The marketing department's cost of producing a amount of televisions is C (x) estimate of the demand function for televisions has not changed and remains p = 10 -0.01x. A) Write an equation for the profit of this company. B) Use the first derivative to find the marginal profit of the function you wrote in part A. C) Compute the second derivative and determine if the value you found in Part B is an absolute maximum or absolute minimum. D) Find the maximum profit of the company. E) At what price are profits maximized?

Consider a housing market in which the rental properties are owned by 10 price-taking compa- nies. The cost function for each company is Jo C(q) = if q ≤ 10 if q> 10. That is, each company can offer any quantity up to its available rental space 10 at no cost, but it cannot offer any more than 10. Suppose the market demand is given by D(p) = 1000 p if p 1000, (c) Determine the point-price elasticities of demand and supply and state whether at the equilibrium price, they are elastic or inelastic. (d) Suppose the government imposes a 20% value added tax on rent. Calculate the equilibrium supply of housing, and determine the price paid by tenants and the price received by housing companies in equilibrium. Does the tax hurt tenants or create a dead- weight loss? Explain your answer!

The Lead Zeppelin Company produces powered and steerable lighter-than-air craft. The company’s airships are specially lined and are therefore safer than normal dirigibles. The table below shows the weekly production of dirigibles, along with the associated Average Cost and Total Revenue figures (the Average Cost and Total Revenue figures are actually in thousands of dollars, so the $15 represents $15,000, but we have left off the zeros to save space).   Quantity Average Cost Total Cost Total Revenue 0  -- 0 $0 1 $15 15 $10 2 $9 18 $20 3 $8 24 $30 4 $8.50 34 $40 5 $9 45 $50 6 $10 60 $60 7 $12 84 $70   The Lead Zeppelin Company has decided that it will produce at least 1 dirigible. Now the question becomes, how many more dirigibles should it produce to make as much profit as possible?   Use the profit-maximizing rule to explain how many dirigibles the Lead Zeppelin Company should produce to…

The FIA ​​Formula 1 World Championship to be held during the 2021 Mexico City Grand Prix has a total cost function equal to CT = Q33 + Q2 + 125Q and an inverse demand function of P = 200−2Q. Now suppose there is a new company managing this event, so the total cost function becomes CT = 4Q. This new company intends to sell at two different prices depending on the place that the spectators occupy at the Hermanos Rodríguez Autodrome. For the Red Zone Boxes. The estimated demand will be q1 = 32−12p1 and for the Green Zone Boxes  It will be q2 = 42 − p2. The number of tickets sold for the Red Zone and Green Zone will be: 15; 84 23; 16 15; 19 33; 45

Q1. Given cost function f(x) = 1/2(c)(x2), where c>0, and demand curve y(z) = z-a, where a > 1 a). Compute price elasticity of demand. b). Draw a diagram showing marginal cost and marginal revenue c). Find price and output that maximize profits d). Find the markup (price divided by marginal cost). Does it increase or decrease based on elasticity of demand?