Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x lawn chairs is R(x) = 0.003x° + 0.01x +0.5x. Currently, Pierce sells 70 lawn chairs daily. a) What is the current daily revenue? b) How much would revenue increase if 75 lawn chairs were sold each day? c) What is the marginal revenue when 70 lawn chairs are sold daily?
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- Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x lawn chairs is R(x)=0.005x³ +0.02x² +0.5x Currently, Pierce sells 90 lawn chairs daily a) What is the current daily revenue? b) How much would revenue increase if 95 lawn chairs were sold each day? c) What is the marginal revenue when 90 lawn chairs are sold daily? d) Use the answer from part (c) to estimate R(91), R(92), and R(93) a) The current revenue is $ b) The revenue would increase by $ (Round to the nearest cent.) c) The marginal revenue is $ when 90 lawn chairs are sold daily. d) R(91) $ R(92) $ R(93) $(b) You are the CEO for a lightweight compasses manufacturer. The demand function 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. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit?Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x lawn chairs is R(x) = 0.006x³ +0.02x² +0.6x. Currently, Pierce sells 90 lawn chairs daily. a) What is the current daily revenue? b) How much would revenue increase if 95 lawn chairs were sold each day? c) What is the marginal revenue when 90 lawn chairs are sold daily? d) Use the answer from part (c) to estimate R(91), R(92), and R(93). (…) a) The current revenue is $ b) The revenue would increase by $. (Round to the nearest cent.) c) The marginal revenue is $when 90 lawn chairs are sold daily. d) R(91) ≈ $ R(92) $ R(93) $
- 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 functionMango 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:5. Demand functions are X-100-Px and Y=152-2Py Total Cost is C-6x2 + 4y2 +4xy + 110, Optimize the profit using two variable regular optimization formula.
- you are an accountant for a manufacterer of radios. the demand function for the tablets is p= 40-4x2 where x is the number of tablets produced in millions. it costs the company $15 to make a tablet. write an equation for the manufactures profit as a function of the number of tablets produced. the company currently produces 1 million tablets and makes a profit of $21000000, but you would like to scale up production a bit, what greater number of tablets could the company produce to yield the same profitA7 You are the manager of a bakery that produces and packages gourmet muffins, and you currently sell muffins in packages of 3. A consultant’s report has estimated the (inverse) demand of a typical consumer to: P = 3 − 0.5Q If your cost of producing bran muffins is C(Q) = Q: (a) What is the marginal cost of muffins? (b) Draw the demand and marginal cost on a diagram. (c) Determine the optimal number of muffins to sell in a single package. (d) What price should the firm charge for each park?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.
- The following graph plots the marginal cost (MC) curve, average total cost (ATC) curve, and average variable cost (AVC) curve for a firm operating in the competitive market for sun lamps. COSTS (Della) 72 04 8 56 24 16 . 0 Price (Dollars per lamp) MOD 8 12 36 48 60 10 ATC AVC 40 00 QUANTITY (Thousands of lamps) For every price level given in the following table, use the graph to determine the profit-maximizing quantity of lamps for the firm. Further, select whether the firm will choose to produce, shut down, or be indifferent between the two in the short run. (Assume that when price exactly equals average variable cost, the firm is indifferent between producing zero lamps and the profit-maximizing quantity of lamps.) Lastly, determine whether the firm will earn a profit, incur a loss, or break even at each price. Quantity (Lamps) ? Produce or Shut Down? Profit or Loss?11:30 l 4G I Homework 4 (section 2.1-2 & 2.2).pdf Economic Mathematics (1) Name ID Section 2.2 Revenue, cost and profit 1. If the demand function of a good is given by P-80 – 3Q, the fixed costs are 100 and variable cost are 5 per unit. Work out the profit when Q-10. 2. Find an expression for the profit function given the demand function 20+P= 25 and the 32 +5. Find the value of 0 for which the firm average cost function AC = (a) breaks even (b) makes a loss of 432 units (c) maximises profit. 2/2 !!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…