(1) A company in Scotland bottles sparkling water. The fixed cost per month to produce bottled water is $35,000, and the variable cost is $0.2 per bottle. Price is related to demand according to the following equation: v = 4,000 – 1.1p Determine the optimal price using a nonlinear profit analysis.
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- 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 profitExercise 4.6 An econometrician hired to analyse a local golf course has determined that there are two types of golfers, the regular and the occasional. The annual demand for games from regular players is given by QH = 24 – 0.3P, where P is the price of a round of golf. On the other hand, the annual demand for occasional items is given by QO = 10 – 0.1P. The marginal cost and the average total cost per item are equal to €20. a) If you could distinguish between regular and casual players, what price would be set for each type? How many games would each type of player play? How much profit could the golf course generate? Represent graphically. b) As an alternative to the discrimination of third degree prices, those in charge consider a double tranche rate according to which the members can play as many games as they wish at a price of € 20 per game. How much profit will the golf course generate if it charges all players the same annual fee for becoming a member of the club? What if you…"The Hickory Cabinet and Furniture Company makes chairs. The fixed cost per month of making chairs is $7,500, and the variable cost per chair is $40. Price is related to demand, according to the following linear equation: v = 400 - 1.2p Graphically illustrate the profit curve developed . Indicate the optimal price and the maximum profit per month.
- Bill runs a business that makes custom-printed towels. It will cost him $8 each to purchase and print on towels, and he will have to pay a rent of $1,700 per month for him workshop. Based on market research, Bill estimates that he can sell custom towels for $25 each. a) Calculate the number of towels he needs to sell per month to break-even. towels b) Calculate the break-even in dollars (round off to the nearest cent).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.A major software developer has estimated the demand for its new personal finance software package to be Q=1,000,000P-2 while the total cost of the package is C = 10,000+ 25Q. If this firm wishes to maximize profit, what percentage markup should it place on this product where percentage markup is defined as 100*(sale price - marginal cost)/marginal cost? 4. a. b. C. d. e. ANS: 90% 100% 20% 40% 250%
- Q1: Analytical part - 8% Best Orange Juice Company is located in Oman. The cost function for total orange juice production (x) is given by C(q) = 0.25x2. Their orange juice is demanded only in Muscat (Muscat demand is Xm- 100-2Pm) and Salalah (Salalah demand is X 100-4Ps). Therefore, the total demand is x-xm+ Xs. If the company can control the quantities supplied to each market, how many should it sell in each location to maximize total profits? What price would it charge in each location? Answer:Nick is planning on starting a mobile pizza oven. He is expecting his customers to spend $20 per pizza. It is estimated that the costs associated with the ingredients will be $5 per pizza. In addition, his fixed costs for renting the mobile oven is $150 per day. 1) How many pizzas does Nick need to sell to break-even per day? 2) If Nick wants to make a profit of $300 and sell 25 pizzas per day, calculate the price he should charge per pizza. 3) If Nick increases the price per pizza to the amount found in part (b) then explain the effect on the break-even number of pizzas sold. Assume the fixed costs and the variable costs remain unchanged. Do not re-calculate the break-even quantity, x, for this question however you may quote the break-even formula and contribution margin to aid your explanation.A startup software company has indicated its cost, c(x), and revenue, f(x), as given below, such that x is the number of lines of programing code (units in 1000 lines). c(x) = 80000 - 2(x-200)2 f(x) = (x-10)3 + (x+10)2 Find the marginal cost analytically, and draw its graph Find the marginal revenue analytically, and draw its graph Solve for the x point where marginal cost is equal to marginal revenue analytically. Comment why is this point significant analytically. Write the profit function and draw its graph Is the profit function concave up or concave down?
- |1.6.1 A company manufactures and sells x dellphones per week. The weekly price-demand and cost equations are given below. p= 400 - 0.5x and C(x) = 20,000 + 140x (A) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? What is the maximum weekly revenue? The company should produce (Round to the nearest cent as needed.) phones each week at a price of $ The maximum weekly revenue is $ (Round to the nearest cent as needed.) (B) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit? What is the maximum weekly profit? The company should produce (Round to the nearest cent as needed.) phones each week at a price of $ The maximum weekly profit is $ (Round to the nearest cent as needed.)Suppose the imaginary company of Roobek is a small, Reno-based American apparel manufacturer specializing in athleisure. The following table presents the brand’s total cost of production at several different quantities. Fill in the remaining cells of the following table. Quantity Total Cost Marginal Cost Fixed Cost Variable Cost Average Variable Cost Average Total Cost (Pairs) (Dollars) (Dollars) (Dollars) (Dollars) (Dollars per pair) (Dollars per pair) 0 120 — — 1 210 2 270 3 315 4 380 5 475 6 630Determine the quantity of output that generates the maximum profit. Use the green points (triangle symbol) to indicate the amount of profit at this quantity of output. Then, determine the quantity of output that generates the maximum total revenue. Use the purple points (diamond symbol) to indicate the amount of revenue at this quantity of output. Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically. Total Revenue, Total Cost 100 90 80 70 50 40 30 20 10 OD 0 O 0 O 0 O 5 10 OF 15 O □ 20 O 25 O 30 TC 35 TR 40 45 50 ♦ Maximum Revenue Maximum Profit (?)