A company supplies a product at two mutually exclusive (do not happen at the same time) periods of time. The demand function for Period 1 is P₁ = 800 - 2Q₁ and the demand function for Period 2 is given by P₂ = 760-2Q₂. The cost for each unit provided is 40 per unit (paid in both markets). Capacity costs 60 per unit and is only paid once and used in both periods. Find the optimal (maximum) profit.
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- Bell Greenhouses has estimated its monthly demand for potting soil to be the following: N=400+4X where N=monthlydemandforbagsofpottingsoil X=timeperiodsinmonths(March2006=0) Assume this trend factor is expected to remain stable in the foreseeable future. The following table contains the monthly seasonal adjustment factors, which have been estimated using actual sales data from the past five years: Forecast Bell Greenhouses demand for potting soil in March, June, August, and December 2007. If the following table shows the forecasted and actual potting soil sales by Bell Greenhouses for April in five different years, determine the seasonal adjustment factor to be used in making an April 2008 forecast.Maha industries produces a product whose anticipated demand for the six periods is 263,256,301, , and the firm has adopted level production strategy with a constant production of 280 units per period. The regular production cost is RO 12 per unit, whereas the overtime and subcontract costs are RO 20 and RO 25 per unit respectively. There is no limit on subcontracting however, maximum overtime production capacity is 10. Average Inventory holding cost RO 5 per unit per period. What will be inventory level at the end of period 3?Q1. Game console manufacturing determines that in order to sell Q units, the price per unit (in dollar) must decreased by the linear demand (the demand function) P(Q)= 800- 0.3Q($/device) The manufacturer also determine that the cost depends on the volume of production and includes a fixed part 500,000($) and a variable part 500Q , that is C(Q)= 500000+ 500Q What price per unit must be charged to get the maximum profit?
- Worldwide annual sales of a device in 2012–2013 were approximately q = −6p + 3,040 million units at a selling price of $p per unit. Assume a manufacturing cost of $40 per unit. [HINT: Recall that Profit = Revenue − Cost.] Find the function P for annual profit, in millions of dollars and in terms of p only, subject to any constraints. P(p) = ____ Find P′(p). P′(p) = ____ What selling price (in dollars) would have resulted in the largest annual profit? (Round your answer to two decimal places.) p = $____ What would have been the resulting annual profit (in millions of dollars)? (Round your answer to the nearest whole number.) $ ____ millionDemand for a company’s product is given by the following equation: Q=1000-0.5P. You are also given that its total cost function TC=100+1000Q. Compute the profit maximizing price and quantity B. A firm earns an accounting profit of K150, 000 per year in project A. The firm could earn K150, 000 and K120, 000 in investments B and C, respectively. How much economic profit is the firm earning assuming the three projects are mutually exclusive?Apply the properties of functions to correctly determine and interpret the break-even point in the following situations, using valid mathematical procedures and correct mathematical notation. Express your answer in terms of the context of the problem. The supply and demand equations for a certain product are: (1) and (2) respectively, where p represents the price per unit in dollars and q, the number of units sold per period. 3q - 200p + 1800 = 0 3q + 100p - 1800 = 0 Algebraically find the equilibrium price. Find and interpret the equilibrium price when a supplier tax of 27 cents per unit is imposed.
- A manufacturer can produce at most 90 units of a certain product each year . The demand equation for the product is p= q2-100q+1800 and the manufacturer's average cost function c=2/3q2-55q+12000/q Determine the profit maximizing output q and the corresponding maximum Profit . The profit maximizing output q is 60In 2012–2015, the price of jet and diesel fuel used by air freight companies decreaseddramatically. As the CEO of FedEx, you have been presented with the following proposals to deal with the situation:a. Reduce shipping rates to reflect the expense reduction.b. Increase the number of deliveries offered per day in some markets.c. Make long-term contracts to buy jet fuel and diesel at a fixed price for the nexttwo years and set shipping rates to a level that will cover these costs.Evaluate these alternatives in the context of the decision-making model presented inthe text.Drives Co. sells portable hard drives. They can sell 600 drives when the price is $75/drive, and they can sell 720 drives when the price is $45/drive. If x represents the number of drives sold, determine the following. (a) What is Drive Co.'s revenue function? R(x) =_ (b)What is the price per drive (in dollars) when revenue is maximized? _ (c) What is the maximum profit (in dollars) made from the sale of these drives if Drive Co. incurs production costs of $165 per drive and has fixed costs of $625? $_
- Demand has grown at Dairy May Farms, and it is considering expanding. One option is to expand by purchasing a verylarge farm that will be able to meet expected future demand.Another option is to expand the current facility by a small amountnow and take a wait-and-see attitude, with the possibility of alarger expansion in two years.Management has estimated the following chances for demand:• Th e likelihood of demand being high is 0.70.• Th e likelihood of demand being low is 0.30.Profi ts for each alternative have been estimated as follows:• Large expansion has an estimated profi tability of either$40,000 or $20,000, depending on whether demand turnsout to be high or low.• Small expansion has a profi tability of $15,000, assuming thatdemand is low.• Small expansion with an occurrence of high demand wouldrequire considering whether to expand further. If thecompany expands at that point, the profi tability is expectedto be $35,000. If it does not expand further, the profi tabilityis…You are the marketing manager of the Business Unit (BU) that produces polystyrene (which is an input to making lightweight rigid foam). The current Demand/Supply balance, as measured by the ICIS price, is $800 per ton of polystyrene. The BU has 2 plants and can produce a total of 1800 tons. At full capacity utilization, the BU’s average variable cost equals $1300/t and its average total cost equals $1700/t. Plant 1 has a capacity of 600 tons and a marginal cost of $900/t. Plant 2 has capacity of 1200 tons and a marginal cost of $1500/t. Due to exit of one competitor, you expect next year’s polystyrene ICIS price to increase to $1200. How much volume of polystyrene do you expect to produce next year, ifany? 2.What is your expected contribution margin for nextyear? 3. What is your expected profit for nextyear?You are the marketing manager of the Business Unit (BU) that produces polystyrene (which is an input to making lightweight rigid foam). The current Demand/Supply balance, as measured by the ICIS price, is $800 per ton of polystyrene. The BU has 2 plants and can produce a total of 1800 tons. At full capacity utilization, the BU’s average variable cost equals $1300/t and its average total cost equals $1700/t.Plant 1 has a capacity of 600 tons and a marginal cost of $900/t. Plant 2 has capacity of 1200 tons and a marginal cost of $1500/t. Due to exit of one competitor, you expect next year’s polystyrene ICIS price to increase to $1200. 1. How much volume of polystyrene do you expect to produce next year, if any? 2. What is your expected contribution margin for next year? 3. What is your expected profit for next year?