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- Q1. A firm faces the following average revenue (demand) curve: P = 100 - 0.01Q where Q is weekly production and P is price, measured in cents per unit. The firm’s cost function is given by C = 50Q + 30,000. Assuming the firm maximizes profits, a. What is the level of production?The aggregate demand for a cup of coffee in Chicago for each day is given by q = 4,000 - 500 p, where p is the price of a cup of coffee. If the price is $4, then the market marginal revenue isThe price-demand equation for the production of bluetooth speakers is: p = 250 - 1/20x, for 0 is less than or equal to x and x is less than or equal to 5000 where x speakers can be sold at $p per each speaker. The cost to produce x speakers is given as C(x) = 150,000 + 30x, where both C(x) and p are represented in dollars ($). - find the profit function and the marginal profit and interpret the quantity P'(4500) - find the marginal cost and interpret the quantity C'(3000) - find the revenue function and the marginal revenue and interpret the quantity R'(3000)
- Suppose the revenue (in dollars) from the sale of x units of a product is given by R(x) = 56x2 + 65x 2x + 2 . Find the marginal revenue when 25 units are sold. (Round your answer to the nearest dollar.)$ Interpret your result. When 25 units are sold, the projected revenue from the sale of unit 26 would be $ .Given Cost and Price (demand) functions C(q)=120q+45000 and p(q)=−2.8q+900, what is the marginal revenue when costs are $80,000? The marginal revenue is ____dollars per item.Question 1a A firm faces the following average revenue (demand) curve: P(Q) = 240 - 0.04 Q where Q is the weekly production and P(Q) is the price, measured in cents per unit. The firm's cost function is given by TC(Q)=120Q+50000. Assume that the firm maximises profit. i) What is the profit maximization quantity and price. ii) What is the total profit per week?
- The demand function for a particular product is given by D(x)=0.5x^2+3x+190‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√D(x)=0.5x^2+3x+190 dollars, where x is the number of units sold. What is the marginal revenue when 88 items are sold? Round your answer to 2 decimal places. D(x)=0.5x^2+3x+190‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾Suppose the demand for a product X produced by a company AAA is given by the following function: QX = 2000 - 250*PX. At what price per item of the product X (EUR) can this copmany maximize its total revenues? Fill in the Table gaps: Demand function Price function Total Revenue (EUR) Marginal Revenue (EUR) Quantity Price per product (EUR) Q = 2000 - 250P P = ? TR = Q*P MR = dTR/dQ = 0 Q = ? P = (2000 - Q)/250 250P = 2000 - Q TR = Q*(2000 - Q)/250 MR = 8 - 2*Q/250 Q/125 = 8 P = (2000 - 1000)/250 P = (2000 - Q)/250 TR = 8*Q - Q^2/250 8 - Q/125 = 0 Q = 1000 P = 4 Alternative solution Demand function Total Revenue (EUR) Marginal Revenue (EUR) Price per product (EUR) Q = 2000 - 250P TR = Q*P MR = dTR/dP = 0 2000 - 500*P = 0 TR = (2000 - 250P)*P MR = 2000 - 2*250*P 500*P = 2000 TR = 2000P - 250P^2 MR = 2000 - 500*P P = 4SANUMARC produces fingerlings for sell. The quantity x (kg) of these fingerlings demanded each week is related to the wholesale unit price p by the equation P = − 0.006x + 180 The weekly total cost incurred by SANUMARC for producing x kgs of fingerlings is C(x) = 0.000002x3 – 0.02x2 + 120x + 60,00 a. Find the marginal cost function C, b. Find the marginal revenue function R’ and the marginal profit function P’ c. Compute P’(2000) and interpret the results.
- There are 1000 pear producers that have identical cost functions, C= 200+0.025q2 where q is the number of crates of apples produced. The producers operate in a perfectly competitive market. The supply curve of each producer is ________ The total supply curve for the market is ________ At a price of 100, the elasticity of supply for the market is _________, meaning that supply is _________ For the answer options, refer to the attached image.A toy manufacturing from has demand for the product is given by the demand function Q= 500 - 3p. Where P is the price in dollars and q is the quantity sold per year. To sell 200 units, what price should the firm charge.Suppose a product's revenue function is given by R(q)=−6q2+400q, where R(q)is in dollars and qis units sold. Also, it's cost function is given by C(q)=103q+3333, where C(q)is in dollars and qis units produced. Find a simplified expression for the item's Marginal Profit function ( MP(q)) and record your answer in the box. Be sure to use the correct variable. (Use the Preview button to check your syntax before submitting your final result). Answer: MP(q)=