Let's say jacky has a demand function for a product made in Ney york city given that the function D(q)=-1.15q+270, where q is the number of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Say that the fixed costs of production for the item is $5,000 and variable costs are $10 per item produced. If 100 items are produced and sold, what are the finds :
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- The demand function for small high-definition televisions is given by p = 9,000 − 55x, where p is the price, in dollars, that x televisions can be sold. The cost function (in dollars) to produce televisions is C = 3,500x + 2,000. (Simplify your answers completely.) (a)Find the revenue function, R. R = (b)Find the profit function, P. P = (c)Find how many televisions should be sold to maximize profit. televisions (d)What is the maximum profit (in dollars)? $*** Please answer e, f, g,h** An ice cream company finds that at a price of $4.00 for each pint, they can sell 4000 pints of ice cream per day. For every $0.25 decrease in price, daily demand increases by 200 units. The company’s cost function is C(q)=0.01q2-90q+211600, where C represents their daily costs (in dollars), and q is the number of pints sold per day. a)Find the demand function q(p). b) Find the revenue function R(q). Hint: first you will need to solve for p in terms of q from the demand function.) c) How many pints should the company sell per day if they want to maximize their revenue? d) what price should the company charge for each pint if they want to maximize their revenue? e)Use the criteria MC(q)=MR(q) to determine how many pints the company should sell per day if they want to maximize their profit. f)What is the maximum profit the company can earn per day? g)Find the average cost function. h)How many pints should the company sell per day if they want to minimize…A manufacturer of a new patented product has found that she can sell 70 units a week direct to the customer if the price is $78. In error, the price was advertised as $138, and, as a result only 40 units were sold in a week. The manufacturer's fixed costs of production are $50 a week and variable costs of $18 per unit. You are required to: a. Show the equation of the demand function linking price(P) to quantity demand(X), assuming it to be a straight line, is P+2X=218 b. Find where the manufacturer breaks even c. Find the quantity that maximizes profit d. Recommend a unit price which would maximize profit e. Determine the maximum profit f. Find the equation of new demand function, assuming a sudden change in trading conditions resulting a 20% reduction in demand at all price levels
- The demand function for a particular brand of LCD TV is given by p = 1480 − 20x where p is the price per unit in dollars when x television sets are sold. (a) Find the revenue function. R(x) = (b) Determine the number of sets that must be sold in order to maximize the revenue.sets(c) What is the maximum revenue? $ (d) What is the price per unit when the revenue is maximized?$ per unitSuppose that the Travnikar Corporation manufactures widgets. Analysts that work for the company have found a function C(x) which reports the cost to produce x widgets and a function R(x) which reports the total revenue from selling x widgets. Currently, the company is producing 500 widgets, but the analysts find that R'(500)=85 and C'(500)=79. In order to maximize profits, should the analysts recommend increasing or decreasing production?A manufacturer of a new patented product has found that he can sell 70 units a week to the customer if the price is $48. In error, the price was recently advertised at $78 and as a result, only 40 units were sold in a week. The manufacturers fixed costs of production are $1,710 a week and variable costs are $9 per unit. You are required to: a. Show the equation of the demand function linking price (P) to quantity demanded (X) assuming it to be a straight line is P = 118-x
- There is a firm making custom stuffed animals. The demand function for custom stuffed animals is: P = 1000 - 20Q The cost depends on how much of each of their inputs they use. It takes 3 inputs to make a stuffed animal: cotton, oil, and chorizo. The amount required, input prices, and restrictions are below: It takes 1 pound of cotton to make a stuffed animal. Cotton costs $20 per pound. They can buy up to 23 pounds of cotton. It takes 2 barrels of oil to make a stuffed animal. Oil costs $10 per barrel. They can buy up to 44 barrels of oil. It takes 3 chorizo burritos to make a stuffed animal. Burritos cost $5 per burrito. They can buy up to 100 burritos. Set this up in Solver to help them maximize profit by choosing the best quantity of stuffed animals to produce, subject to the constraints of the maximum amount of cotton/oil/burritos they can buy. In the space below, tell the profit that the firm will earn when they maximize its profit. PLEASE SHOW EXCEL WALKTHROUGH USING SOLVER.…Suppose the demand function for a product is given by the function: D ( q ) = − 0.02 q + 80 D ( q ) = - 0.02 q + 80 Use integration (or other appropriate methods) to find the following: (Do no rounding of results until the very end of your calculations. At that point, round to the nearest tenth, if necessary. It may help you to sketch the demand curve, which crosses the horizontal at q = 4 , 000 q = 4 , 000 .) A) The total actual revenue for q = 3 , 350 q = 3 , 350 units: Answer 1: B) The total possible revenue (for all quantities and prices): Answer 2: C) The Consumer's surplus corresponding to q = 3 , 350 q = 3 , 350 units: Answer 3: D) The "Not Sold" value corresponding to q = 3 , 350 q = 3 , 350 units: Answer 4The demand and supply functions for coal are given as: (In pictures) what is the inverse demand function? what is the inverse supply function?
- ) 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?A firm manufactures two goods labeled 1 and 2. It sells Qi items of good i for a fixed price per unit of pi. The total cost of producing good i is ciQi2.Explain briefly why the profit function is given byπ(Q1, Q2) = p1Q1 + p2Q2 − c1Q12 − c2Q22Find the values of Q1 and Q2 which maximize π and verify that the second-order conditions for a maximum are satisfied. Find an expression for the maximum profit.A commodity has a demand function modeled by p = 106 − 0.5x and a total cost function modeled by C = 30x + 33.75, where x is the number of units. (a) What unit price (in dollars) yields a maximum profit? $ per unit (b) When the profit is maximized, what is the average cost (in dollars) per unit? (Round your answer to two decimal places.) $ per unit