HITACHI LTD. an air conditioner manufacturer, produces 'x' sets per week at a total cost of x²+780x+25000. The firm is a monopolist and the demand function for its product is x = (15000 - P), where the price is 'p' per set. (i) Determine the number of AC sets to be produced per week at which the firm will earn maximum net revenue; and (ii) Decide the monopoly price.
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- Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.Referring to Example 11.1, if the average bid for each competitor stays the same, but their bids exhibit less variability, does Millers optimal bid increase or decrease? To study this question, assume that each competitors bid, expressed as a multiple of Millers cost to complete the project, follows each of the following distributions. a. Triangular with parameters 1.0, 1.3, and 2.4 b. Triangular with parameters 1.2, 1.3, and 2.2 c. Use @RISKs Define Distributions window to check that the distributions in parts a and b have the same mean as the original triangular distribution in the example, but smaller standard deviations. What is the common mean? Why is it not the same as the most likely value, 1.3?
- Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?(1) When chef Paolo prices his speciality ‘pizza-n-all’ meal at £25, he sells 20 meals a day. When he prices his pizza meal at £22, he sells 21 meals a day. Suppose Paolo reduces his price from £25 to £22. Explain the impact of the price reduction on the revenue he receives from the first 20 meals he sells. Total Revenue – Price X Quantity. Revenue @ £25 = £25 X 20 = £500. Revenue @ £22 = £25 X 20 = £440 The impact of the price reduction is a reduction in total revenue of £60 (-12%) over the first 20 meals that he sells. Calculate the additional revenue generated from the additional meals he sells when he lowers his price to £22. Total Revenue = Price X Quantity. Total Revenue @ £22 = £22 X 21 = £462. Additional Revenue = Revenue @ £25 – revenue @ £22 = £500 - £462 = -£38. Calculate the marginal revenue Paolo receives from the 21st meal. How does that amount relate to the amounts you calculated in (a) and (b)? (3%) Suppose Paolo reduces his price from £25 to £22. Explain…Assume the demand for a company’s drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year,it will cost $16x. Each unit of Wozac is soldfor $3. Each unit of Wozac produced -incurs a variable production cost of $0.20. It costs $0.40 per year to operate a unit of capacity.Determine how large a Wozac plant the company should build to maximize its-expected profit over the next 10 years.
- Sodaco is considering producing a new product:Chocovan soda. Sodaco estimates that the annual demandfor Chocovan, D (in thousands of cases), has the followingmass function: P(D 30) .30, P(D 50) .40,P(D 80) .30. Each case of Chocovan sells for $5 andincurs a variable cost of $3. It costs $800,000 to build aplant to produce Chocovan. Assume that if $1 is receivedevery year (forever), this is equivalent to receiving $10 atthe present time. Considering the reward for each action andstate of the world to be in terms of net present value, useeach decision criterion of this section to determine whetherSodaco should build the plant.A company manufactures two products. If it charges aprice pi for product i, it can sell qi units of product i, whereq1 60 3p1 p2 and q2 80 2p2 p1. It costs $25to produce a unit of product 1 and $72 to produce a unit ofproduct 2. How many units of each product should beproduced to maximize profits?A company manufactures two products. If it chargesprice pi for product i, it can sell qi units of product i,where q1 = 60 - 3p1 + p2 and q2 = 80 - 2p2 + p1. Itcosts $5 to produce a unit of product 1 and $12 to produce a unit of product 2. How many units of eachproduct should the company produce, and what pricesshould it charge, to maximize its profit? Use spreadsheet modelling in Excel
- 3-2) The optimal quantity of the three products and resulting revenue for Taco Loco is: A) 28 beef, 80 cheese, and 39.27 beans for $147.27. B) 10.22 beef, 5.33 cheese, and 28.73 beans for $147.27. C) 1.45 Z, 8.36 Y, and 0 Z for $129.09. D) 14 Z, 13 Y, and 17 X for $9.81. 3-3) Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix? A) 26 to 38.22 pounds B) 27.55 to 28.45 pounds C) 17.78 to 30 pounds D) 12.22 to 28 poundsA company produces and sells luxury goods and is able to control the demand for the product by varying the selling price. The relationship between price and demand is found to be p = 10 − 42 D2 + 2D where p is the price per unit in million dollars and D is the demand per year. The company is seeking to maximize its profit. The fixed cost is $59 million per year and the variable cost is $25 million per unit. The production capacity is 42 units per year, and the company produces at least 1 unit per month. a) Derive how to find the number of units that should be produced annually to maximize profit. b) What is the maximum profit per year? c) What is the annual breakeven point? d) What is the company’s range of profitable output per year?A retired couple supplement their income by making fruit pies, which they sell to a local grocery store. During the month of September, they produce apple and grape pies. The apple pies are sold for $1.50 to the grocer, and the grape pies are sold for $1.20. The couple is able to sell all of the pies they produce owing to their high quality. They use fresh ingredients. Flour and sugar are purchased once each month. For the month of September, they have 1,200 cups of sugar and 2,100 cups of flour. Each apple pie requires 1 1⁄2 cups of sugar and 3 cups of flour, and each grape pie requires 2 cups of sugar and 3 cups of flour. a. Determine the number of grape and the number of apple pies that will maximize revenues if the couple working together can make an apple pie in six minutes and a grape pie in three minutes. They plan to work no more than 60 hours. b. Determine the amounts of sugar, flour, and time that will be unused.