Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 7.3, Problem 12P
a)
Summary Introduction
To identify: If the changes in optimal solution are in the direction as expected.
Non-linear programming (NLP):
Non-linear programming (NLP) is used in complex optimization problems where the objectives or constraints or sometimes both are non-linear functions of the decision variables. A model can be termed as non-linear for more than one reason.
b)
Summary Introduction
To identify: If the changes in optimal solution are in the direction as expected for different magnitudes.
c)
Summary Introduction
To make: The changes simultaneously and return the results.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
(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…
Producers of a certain brand of refrigerator will make 4000 refrigerators available when the unit price is $340. At a unit price of $380, 8000 refrigerators will be marketed. Find the equation relating the unit price p of a refrigerator to the quantity supplied x if the equation is known to be linear.p =
How many refrigerators will be marketed when the unit price is $420?refrigeratorsWhat is the lowest price at which a refrigerator will be marketed?$
The Camera Shop sells two popular models of digital SLR cameras (Camera A Price: 220, Camera B Price: 310). The sales of these products are not independent of each other, but rather if the price of one increase, the sales of the other will increase. In economics, these two camera models are called substitutable products. The store wishes to establish a pricing policy to maximize revenue from these products. A study of price and sales data shows the following relationships between the quantity sold (N) and prices (P) of each model:
NA = 196 - 0.5PA + 0.35PB
NB = 301 + 0.06PA - 0.6PB
Construct a model for the total revenue and implement it on a spreadsheet. Develop a two-way data table to estimate the optimal prices for each product in order to maximize the total revenue. Vary each price from $250 to $500 in increments of $10.
Max profit occurs at Camera A price of $ .
Max profit occurs at Camera B price of $ .
Check My Work (3 remaining)
Chapter 7 Solutions
Practical Management Science
Ch. 7.3 - Prob. 1PCh. 7.3 - Prob. 2PCh. 7.3 - Pricing Decisions at Madison The Madison Company...Ch. 7.3 - Prob. 4PCh. 7.3 - Prob. 5PCh. 7.3 - Prob. 6PCh. 7.3 - Prob. 7PCh. 7.3 - Prob. 8PCh. 7.3 - Prob. 9PCh. 7.3 - Prob. 10P
Ch. 7.3 - Prob. 11PCh. 7.3 - Prob. 12PCh. 7.3 - Prob. 13PCh. 7.3 - PRICING SUITS AT SULLIVANS Sullivans is a retailer...Ch. 7.3 - Prob. 15PCh. 7.4 - Prob. 16PCh. 7.4 - Prob. 17PCh. 7.4 - Prob. 18PCh. 7.4 - Prob. 19PCh. 7.4 - Prob. 20PCh. 7.4 - Prob. 21PCh. 7.4 - Prob. 22PCh. 7.4 - Prob. 23PCh. 7.5 - Prob. 24PCh. 7.5 - Prob. 25PCh. 7.5 - Prob. 26PCh. 7.5 - Prob. 27PCh. 7.6 - Prob. 28PCh. 7.6 - Prob. 29PCh. 7.6 - Prob. 30PCh. 7.6 - Prob. 31PCh. 7.6 - Prob. 32PCh. 7.6 - Prob. 33PCh. 7.6 - The method for rating teams in Example 7.8 is...Ch. 7.7 - Prob. 35PCh. 7.7 - Prob. 36PCh. 7.7 - Prob. 37PCh. 7.7 - The stocks in Example 7.9 are all positively...Ch. 7.7 - Prob. 39PCh. 7.7 - Prob. 40PCh. 7.7 - Prob. 41PCh. 7.7 - Prob. 42PCh. 7.8 - Given the data in the file Stock Beta.xlsx,...Ch. 7.8 - Prob. 44PCh. 7 - Prob. 45PCh. 7 - Prob. 46PCh. 7 - Another way to derive a demand function is to...Ch. 7 - Prob. 48PCh. 7 - If a monopolist produces q units, she can charge...Ch. 7 - Prob. 50PCh. 7 - Prob. 51PCh. 7 - Prob. 52PCh. 7 - Prob. 53PCh. 7 - Prob. 54PCh. 7 - Prob. 55PCh. 7 - Prob. 56PCh. 7 - A beer company has divided Bloomington into two...Ch. 7 - Prob. 58PCh. 7 - Prob. 59PCh. 7 - Prob. 60PCh. 7 - Prob. 61PCh. 7 - Prob. 62PCh. 7 - Prob. 63PCh. 7 - You have 50,000 to invest in three stocks. Let Ri...Ch. 7 - Prob. 65PCh. 7 - Prob. 66PCh. 7 - Prob. 67PCh. 7 - Prob. 68PCh. 7 - Prob. 69PCh. 7 - Prob. 70PCh. 7 - Based on Grossman and Hart (1983). A salesperson...Ch. 7 - Prob. 73PCh. 7 - Prob. 74PCh. 7 - Prob. 75PCh. 7 - Prob. 76PCh. 7 - Prob. 77PCh. 7 - Prob. 78PCh. 7 - Prob. 79PCh. 7 - Prob. 80PCh. 7 - Prob. 81PCh. 7 - Prob. 82PCh. 7 - Prob. 83PCh. 7 - Prob. 84PCh. 7 - Prob. 85PCh. 7 - Prob. 86PCh. 7 - Prob. 1.1CCh. 7 - Prob. 1.2CCh. 7 - Prob. 1.3CCh. 7 - Prob. 1.4C
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.Similar questions
- The shadow price is calculated to be P4.00 for a less than or equal to constraint in a maximization LP problem with the optimal objective function value of z = 25, this means that a.if the coefficient of the objective function is increase by 1 then the RHS for that constraint must be increased by 4. b. if the RHS for that constraint is increased by 4 units then the optimal objective function value will become 26 c.if the coefficient of the objective function is increase by 4 then the RHS for that constraint must be increased by 1. d.if the RHS for that constraint is increased by one unit then the optimal objective function value will become 29arrow_forwardA market analyst working for a small appliance manufacturer finds that if the firm produces and sells x blenders annually, a model for the total profit (in dollars) is P(x) = 8x + 0.3x2 − 0.001x3 − 372. Graph the function P in an appropriate viewing rectangle, and use the graph to answer the following questions. (a) When just a few blenders are manufactured, the firm loses money (profit is negative). (For example, P(10) = −263, so the firm loses $263.00 if it produces and sells only 10 blenders.) How many blenders must the firm produce to break even? (Round your answer to the nearest whole number.) blenders(b) Does profit increase indefinitely as more blenders are produced and sold? YesNo If not, what is the largest possible profit the firm could have? (If profit increases indefinitely, enter your answer as ∞. Otherwise, round your answer to the nearest cent.)arrow_forward(i) A consumer has income of £3,000. Apple juice is priced at £3 a bottle and cheese is priced at £6 a kilo. Drawthe budget constraint for a consumer with standard preferences. What is the slope of this budget constraint? (ii) Show a consumer’s budget constraint and indifference curves for apple juice and cheese. Show the optimalconsumption choice. If the price of juice is £3 a bottle and the price of cheese is £6 a kilo, what is the marginalrate of substitution at this optimum? (iii) The price of cheese rises from £6 to £10 a kilo, while the price of juice remains at £3 a bottle. For aconsumer with a constant income of £3,000, show what happens to consumption of juice and cheese.Decompose the change into income and substitution effects.arrow_forward
- Another way to derive a demand function is to break the market into segments and identify a low price, a medium price, and a high price. For each of these prices and market segments, we ask company experts to estimate product demand. Then we use Excels trend curve fitting capabilities to fit a quadratic function that represents that segments demand function. Finally, we add the segment demand curves to derive an aggregate demand curve. Try this procedure for pricing a candy bar. Assume the candy bar costs 0.55 to produce. The company plans to charge between 1.10 and 1.50 for this candy bar. Its marketing department estimates the demands shown in the file P07_47.xlsx (in thousands) in the three regions of the country where the candy bar will be sold. What is the profit-maximizing price, assuming that the same price will be charged in all three regions?arrow_forwardIf 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%.arrow_forwardThe stocks in Example 7.9 are all positively correlated. What happens when they are negatively correlated? Answer for each of the following scenarios. In each case, two of the three correlations are the negatives of their original values. Discuss the differences between the optimal portfolios in these three scenarios. a. Change the signs of the correlations between stocks 1 and 2 and between stocks 1 and 3. (Here, stock 1 tends to go in a different direction from stocks 2 and 3.) b. Change the signs of the correlations between stocks 1 and 2 and between stocks 2 and 3. (Here, stock 2 tends to go in a different direction from stocks 1 and 3.) c. Change the signs of the correlations between stocks 1 and 3 and between stocks 2 and 3. (Here, stock 3 tends to go in a different direction from stocks 1 and 2.) EXAMPLE 7.9 PORTFOLIO SELECTION AT PERLMAN BROTHERS Perlman Brothers, an investment company, intends to invest a given amount of money in three stocks. From past data, the means and standard deviations of annual returns have been estimated as shown in Table 7.2. The correlations among the annual returns on the stocks are listed in Table 7.3. The company wants to find a minimum-variance portfolio that yields a mean annual return of at least 0.12.arrow_forward
- This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.arrow_forwardSelect all of the true statements: When we successfully find a solution to a linear programming problem (using the Simplex LP method) with Solver, we cannot guarantee that the solution obtained is an optimal solution. If all the supplies and demands for a transportation model are integers, then the optimal Solver solution may or may not have integer-valued shipments. In transportation problem, shipping costs are often nonlinear due to quantity discounts. RISKSIMTABLE is a function in @RISK for running several simulations simultaneously, one for each setting of an input or decision variable. One of the primary advantages of simulation models is that they enable managers to answer what-if questions about changes in systems without actually changing the physical systems themselves. When we solve a nonlinear programming problem (NLP), it is very possible that Solver will obtain a suboptimal solution. A correlation matrix must always have 1’s along its diagonal (because a variable is…arrow_forwardShow cells in excel with step by step using solver and the sum product function show how to calculate weighted risk Wall Street firms commonly use linear programming models to select their bond portfolios. A firm is considering the following 5 bonds: Bond Annual Return rate (%) Risk measure Bond 9.2 5 Bond 5 3 Bond 6.1 2 Bond 3.5 4 Bond 1.2 1 In the table above, “risk measure” has a value between 1 and 5 with 5 indicating the riskiest bond and 1 the least risky bond. The firm has a budget of 1 million dollars for this investment. The firm wants to decide its investments in the 5 bonds to maximize the expected return of the portfolio, subject to constraints listed below: The weighted average risk of the portfolio should not exceed 4. At least 30% of the total investment can be invested in bond 3. To diversify the portfolio, the investment on each bond should be at least 10% of the total investment. The sum of investments made in…arrow_forward
- A firm is considering importing some products to sell in a local market. The unit price and cost for product i are p; and Cį, respectively. While the prices may be determined by the firm, the costs are given and fixed. For product i, the demand volume is Aį – Bipi, where A; and Bi are all given. The amount of budget that may be used to purchase all products is K. The demand volume may be fractional. Formulate a mathematical program that can find a purchasing plan that maximizes the firm's profit. Determine whether your program is an LP, IP, or NLP.arrow_forwardSelect the best statement if we consider the following situation: The right-hand side of a particular constraint is 30. Applying sensitivity analysis to the LP model shows that the shadow price is 1.2 and an allowable increase of 15 and allowable decrease of 10. 1.If 20≤RHS≤45, the change in the objective function value will be 1.2 times the difference between the new value and 30. 2.If 10≤RHS≤15, the change in the objective function value will be 1.2 times the difference between the new value and 30. 3.The objective function value will increase. 4.The objective function value will decrease.arrow_forwardD) Because of increased competition, Deegan is considering reducing the price of model DRB such that the new contribution to profit is $175 per unit. How would this change in price affect the optimal solution? Explain. The objective coefficient range for model DRB shows a lower limit of $______ . Thus, the optimal solution (will/will not) change and the new value will be $______ . E) If the available manufacturing time is increased by 500 hours, will the dual value for the manufacturing time constraint change? Explain. The allowable increase is _____ minutes, so the dual value for this constraint (will/will not) change. Just please fill in the blanks thank you.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,
Practical Management Science
Operations Management
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:Cengage,