The demand and total profit function, P(x) for rooms in a hotel are given as follows. 3x = 600 - P P(x) = 450x – 3.5x2 - 4000 Where p is the price in ringgit per room and x is the quantity of room rented. Determine the marginal cost when 2 rooms are rented
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The demand and total profit function, P(x) for rooms in a hotel are given as follows.
3x = 600 - P
P(x) = 450x – 3.5x2 - 4000
Where p is the price in ringgit per room and x is the quantity of room rented. Determine the marginal cost when 2 rooms are rented
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- A company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500 per day when producing 15 sinks. The company has a daily demand function of q = 360 − p, where q is the number if laundry sinks demanded and p is te price of a laundry sink. (d) How many laundry sinks will the company need to produce in order to maximise it′s profits?A firm has a linear demand function for it's product.When the price for the product is Sh.220,the quantity demanded is 40 units.When the price increases to Sh.240 the quantity demanded becomes 30 units.In addition,the firm's marginal cost function is given by; MC = 40Q-2Q^2+2 Fixed cost = Sh. 5 million Where Q= quantity demanded, Mc= marginal cost(cost in Sh. Million) Required 1.The level of output that maximises profits 2.The maximum profit 3.The price of the product at a maximum profitIt costs a coat manufacturer $8750 to make 125 coats and it costs $6500 to make 80 coats. Each coat is sold for $250. a. How much is the marginal cost? Round to two decimal places if rounding is necessary. Do not enter a fraction. There is a $ sign next to the answer box, so do not type a $ sign in your answer. Only type a number (do not type any units on your answer). $ b. What is the slope of the Profit function, P(x)? Round to two decimal places if rounding is necessary. Do not enter a fraction. There is a $ sign next to the answer box, so do not type a $ sign in your answer. Only type a number (do not type any units on your answer). $ c. How many coats must be sold in order to break even? Round to the nearest whole number if rounding is necessary. Do not enter a fraction. Only type a whole number (do not type any units on your answer).
- A company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500 per day when producing 15 sinks. The company has a daily demand function of q = 360 − p, where q is the number if laundry sinks demanded and p is te price of a laundry sink. (e) What is the maximum profit?Your college newspaper, The Collegiate Investigator, sells for 90¢ per copy. The cost of producing x copies of an edition is given by C(x) = 70 + 0.10x + 0.001x2 dollars. (a) Calculate the marginal revenue R'(x) and profit P'(x) functions. HINT [See Example 2.] R'(x) = P'(x) = (b) Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 500 copies of the latest edition. revenue $ profit $ marginal revenue $ per additional copy marginal profit $ per additional copy Interpret the results. The approximate from the sale of the 501st copy is $ . (c) For which value of x is the marginal profit zero?x = copiesInterpret your answer. The graph of the profit function is a parabola with a vertex at x = , so the profit is at a maximum when you produce and sell copies.A firm has a linear demand function for it's product.When the price of the product is sh.20,the quantity demanded is 40 units.When the price increases to sh.240 the quantity demanded becomes 30 units.In addition,the firm's marginal cost function is giving by: Mc = 40q- 2q^2+2 Fixed cost = 5 million Where q= quantity demanded,Mc = marginal cost(sh.million) Required 1.The level of output that maximises profits 2.The maximum profit 3.The price of the product at the maximum profit
- *** 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…Suppose that the marginal revenue for a product is MR = 775 and the marginal cost is MC = 39 times sq. root of x+1, with a fixed cost of $906. Find the profit function, then find the profit or loss fromthe production and sale of 3 units.__________________________________________________A firm has a linear demand function for its product. When the price of the product isSh.220, the quantity demanded is 40 units. When the price increases to Sh.240, thequantity demanded becomes 30 units. In addition, the firm’s marginal cost function isgiven by:MC = 40q – 2q2 + 2Fixed cost = Sh.5 millionWhere q = quantity demanded, MC = marginal cost (Sh. million)Evaluate the level of output that maximizes profits.
- For a firm’s product, the demand function is p =72−0.04q and the average cost function is i. ¯ c = 500 q +30 i. At what level of output would profit be maximized? ii. ii. Atwhat price is the profit maximized?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.Sergio Lopez is a publisher of Latin American poetry. His fixed cost is $525, and the cost to produce each individual copy of his book is $3.50. Currently, Sergio is selling these books for $6 each. So far this year, he has produced x a. Write a linear cost function C for Sergio’s book production, in terms of x. b. Find the linear revenue function R for selling x copies of the book. Remember that P(x) = (price)x. c. Use and 1b. to determine the profit function P for selling x books. Write the formula in simplified form. d.Use your answer for 1c to determine the profit, in dollars, for selling 300 books.
