Suppose the distribution of home sales prices has mean k300, 000 and standard deviation of k50, 000. (i) Determine the price range in which at least 75% of the houses sold. (ii) Determine the minimum percentage of the houses that should sell for prices between k150, 000 and k450, 000. (iii) Determine the minimum percentage of the houses that should sell for prices between k170, 000 and k430, 000.
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Suppose the distribution of home sales prices has mean k300, 000 and standard
deviation of k50, 000.
(i) Determine the price range in which at least 75% of the houses sold.
(ii) Determine the minimum percentage of the houses that should sell for
prices between k150, 000 and k450, 000.
(iii) Determine the minimum percentage of the houses that should sell for
prices between k170, 000 and k430, 000.
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- PRICING SUITS AT SULLIVANS Sullivans is a retailer of upscale mens clothing. Suits cost Sullivans 320. The current price of suits to customers is 350. which leads to annual sales of 300 suits. The elasticity of the demand for mens suits is estimated to be 2.5 and assumed to be constant over the relevant price range. Each purchase of a suit leads to an average of 2.0 shirts and 1.5 ties being sold. Each shirt contributes 25 to profit, and each tie contributes 15 to profit. Determine a profit-maximizing price for suits. In the complementary-product pricing model in Example 7.3, we have assumed that the profit per unit from shirts and ties is given. Presumably this is because the prices of these products have already been set. Change the model so that the company must determine the prices of shirts and ties, as well the price of suits. Assume that the unit costs of shirts and ties are, respectively, 20 and 15. Continue to assume that, on average, 2.0 shirts and 1.5 ties are sold along with every suit (regardless of the prices of shirts and ties), but that shirts and ties have their own separate demand functions. These demands are for shirts and ties purchased separately from suit purchases. Assume constant elasticity demand functions for shirts and ties with parameters 288,500 and 1.7 (shirts), and 75,460 and 1.6 (ties). Assume the same unit cost and demand function for suits as in Example 7.3. a. How much should the company charge for suits, shirts, and ties to maximize the profit from all three products? b. The assumption that customers will always buy, on average, the same number of shirts and ties per suit purchase, regardless of the prices of shirts and ties, is not very realistic. How might you change this assumption, and change your model from part a accordingly, to make it more realistic?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.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?
- 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%.In Problem 12 of the previous section, suppose that the demand for cars is normally distributed with mean 100 and standard deviation 15. Use @RISK to determine the best order quantityin this case, the one with the largest mean profit. Using the statistics and/or graphs from @RISK, discuss whether this order quantity would be considered best by the car dealer. (The point is that a decision maker can use more than just mean profit in making a decision.)Thorne Estates Limited advertises and sells residential property on behalf of its customers. The company has been in business for only a short time and is preparing a cash budget for first four months of 2021. Expected sales of residential properties are as follows: 2020 2021 Month Dec Jan Units Sold 10 10 2021 2021 2021 Feb Mar Apr 15 25 30 The average price of each property is £180,000 and Thorne Estates charges a fee of 3% of the value of each property sold. Thorne Estates receives a 1% in the month of sale and the remaining 2% in the month after sale. The company has nine employees who are paid on a monthly basis. The average salary per employee is £35,000 per year. If more than 20 properties are sold in a given month, each employee is paid in that month a bonus of £140 for each additional property sold. Variable expenses are incurred at the rate of 0.5% of the value of each property sold and these expenses are paid in the month of sale. Fixed overheads of £4,300 per…
- A purchasing agent for a particular type of silicon wafer used in the production ofsemiconductors must decide among three sources. Source A will sell the siliconwafers for $2.50 per wafer, independently of the number of wafers ordered. Source Bwill sell the wafers for $2.40 each but will not consider an order for fewer than3,000 wafers, and Source C will sell the wafers for $2.30 each but will not acceptan order for fewer than 4,000 wafers. Assume an order setup cost of $100 and anannual requirement of 20,000 wafers. Assume a 20 percent annual interest rate forholding cost calculations.c. If the replenishment lead time for wafers is three months, determine the reorderpoint based on the on-hand level of inventory of wafersA purchasing agent for a particular type of silicon wafer used in the production ofsemiconductors must decide among three sources. Source A will sell the siliconwafers for $2.50 per wafer, independently of the number of wafers ordered. Source Bwill sell the wafers for $2.40 each but will not consider an order for fewer than3,000 wafers, and Source C will sell the wafers for $2.30 each but will not acceptan order for fewer than 4,000 wafers. Assume an order setup cost of $100 and anannual requirement of 20,000 wafers. Assume a 20 percent annual interest rate forholding cost calculations.b. What is the optimal value of the holding and setup costs for wafers when theoptimal source is used?A purchasing agent for a particular type of silicon wafer used in the production ofsemiconductors must decide among three sources. Source A will sell the siliconwafers for $2.50 per wafer, independently of the number of wafers ordered. Source Bwill sell the wafers for $2.40 each but will not consider an order for fewer than3,000 wafers, and Source C will sell the wafers for $2.30 each but will not acceptan order for fewer than 4,000 wafers. Assume an order setup cost of $100 and anannual requirement of 20,000 wafers. Assume a 20 percent annual interest rate forholding cost calculations.a. Which source should be used, and what is the size of the standing order?
- (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…A 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?Suppose a certain manufacturing company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,400, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,900. Manufacturing costs are $13 for each 4-cylinder connecting rod and $19 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 6,000 6-cylinder connecting rods and 8,000 4-cylinder connecting rods. Let x4 = the number of 4-cylinder connecting rods produced next week x6 = the number of 6-cylinder connecting rods produced next week s4 = 1 if the production line is set up to…