Concept explainers
a)
To determine: The range of feasibility for each constraint.
Introduction:
Linear programming:
Linear programming is a mathematical modelling method where a linear function is maximized or minimized taking into consideration the various constraints present in the problem. It is useful in making quantitative decisions in business planning.
Range of feasibility:
It is the range of the values present in the right hand side quantities of a constraint. The shadow prices and variables attained in the solution will remain the same for the right hand side quantities.
b)
To determine: The range of optimality for the coefficients of the objective function.
Introduction:
Linear programming:
Linear programming is a mathematical modelling method where a linear function is maximized or minimized taking into consideration the various constraints present in the problem. It is useful in making quantitative decisions in business planning.
Range of optimality:
It is the range of values at which the coefficient of the objective function of a decision variable will change without changing either the list of the variables in the optimal quantities or the solution.
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Chapter 19 Solutions
OPERATIONS MANAGEMENT (LL) W/CONNECT
- Formulate decision variable, objective function, and constraints only. Eastborne Realty has $2 million available for the purchase of new rental property. After an initial screening, Eastborne reduced the investment alternatives to townhouses and apartment buildings. Each townhouse can be purchased for $282,000, and five are available. Each apartment building can be purchased for $400,000, and the developer will construct as many buildings as Eastborne wants to purchase. Eastborne’s property manager can devote up to 140 hours per month to these new properties; each townhouse is expected to require 4 hours per month, and each apartment building is expected to require 40 hours per month. The annual cash flow, after deducting mortgage payments and operating expenses, is estimated to be $10,000 per townhouse and $15,000 per apartment building. Eastborne’s owner would like to determine the number of townhouses and the number of apartment buildings to purchase to maximize annual cash flow.arrow_forwardJane is planning to buy a new car for her work as a trader. After narrowing her choices down to three models (X, Y, and Z) within her budget, she is having difficulty in deciding which one to purchase. She has compared each model against one another on the basis of four criteria: price, safety, economy, and comfort. Her comparisons are summarised below:arrow_forwardFormulate and prove a sufficient condition for optimality for an infinite-horizon problem.arrow_forward
- Monica and Isabel are roommates who, on this particular Saturday morning, are trying to decide what scarf to wear. Each has a Burberry scarf (which we’ll denote B), a tan scarf (denoted T), and a mauve scarf (denoted M). They care about the scarf but also about whether they end up wearing the same or different scarves. The preference ordering (from best to least preferred outcome) for Monica is: (1) she wears B and Isabel wears T or M; (2) she wears T and Isabel wears B or M; (3) she wears B and Isabel wears B; (4) she wears T and Isabel wears T: (5) she wears M and Isabel wears M; and (6) she wears M and Isabel wears B or T. Isabel’s preference ordering is: (1) she wears T and Monica wears B or M; (2) she wears M and Monica wears B or T; (3) she wears T and Monica wears T; (4) she wears M and Monica wears M; (5) she wears B and Monica wears B; and (6) she wears B and Monica wears T or M. Applying the IDSDS, which scarves will be worn?arrow_forwardA local real estate investor in Kingston is considering three alternative investments: a motel, a restaurant, or a theater. Profits from the motel or restaurant will be affected by the availability of gasoline and the number of tourists; profits from the theater will be relatively stable under any conditions. The following payoff table shows the profit or loss that could result from each investment: Real Estate Investor Payoff Table Payoffs are Profits States of Nature (Gasoline Availability) Decision Alternatives Shortage Stable Supply Surplus Motel $–8,000 $15,000 $22,000 Restaurant $2,000 $8,000 $6,000 Theater $6,000 $6,000 $5,000 Which option should the real estate investor choose if he uses the LaPlace criterion? Using…arrow_forwardFormulate the objective function and constraints function for the problemarrow_forward
- 5. A professional basketball team just missed making the playoffs last season and believes it only needs to sign one very good free agent to make the playoffs next season. The team is considering four players: Morris, O'Neal, Jackson, and Gordon. Each player differs according to position, ability, and attractiveness to fans. The payoffs (in $ millions) to the team for each player based on their contract, profits from attendance, and team product sales for several different seasonal outcomes are provided in the following table. Season Outcome Loser Competitive | Playoffs $1.3 $4.4 1.8 6.3 0.7 5.8 -1.6 9.6 Player Morris $-3.2 O'Neal -5.1 Jackson -2.7 Gordon -6.3 Determine the best decision using the following decision criteria. a) Maximax b) The management has determined the following probabilities of the occurrence of each future seasonal outcome for each player: Probability Loser Competitive Playoffs 0.55 0.30 0.26 0.56 0.32 0.47 0.25 0.45 Player Morris 0.15 O'Neal 0.18 Jackson 0.21…arrow_forwardProblem 8-21 (Algorithmic) Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows: Rental Class Room Super Saver Deluxe Business Type I $30 $35 — Type II $20 $30 $40 Type I rooms do not have wireless Internet access and are not available for the Business rental class. Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 130 rentals in the Super Saver class, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms. Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be…arrow_forwardObtain the initial basic feasible solution using all the three methods.arrow_forward
- Calculating outcomes as equally likely would BEST describe: O a. Maximax criterion O b. Laplace criterion O c. Regret criterion Od. Maximin criterion Determining the average payoff for each alternative and choosing the one with the BEST payoff is the approach called: ea, maximax O b. minimax regret O c. laplace Od maximin 2arrow_forwardFormulate the Linear Programming algebraic model : The DLSU Faculty Cooperative has P250,000 available to invest in a 12-month commitment. The money can be placed in Treasury notes yielding an 8% return or in municipal bonds at an average rate of return of 9%. Cooperatives regulations require diversification to the extent that at least 50% of the investment be placed in Treasury notes. Because of restrictions of Bureau of Internal Revenue, it is decided that no more than 40% of the investment be placed in bonds. Determine the budget that should be allocatedarrow_forwardA local real estate investor in Montego Bay is considering three alternative investments: a motel,a restaurant, or a theatre. Profits from the motel or restaurant will be affected by the availabilityof gasoline and the number of tourists; profits from the theatre will be relatively stable under anyconditions. The following payoff table shows the profit or loss that could result from eachinvestment: Real Estate Investor Payoff Table Payoffs are Profits States of Nature (Gasoline Availability)Decision Alternatives Shortage Stable Supply SurplusMotel $–8,000 $15,000 $20,000Restaurant $2,000 $8,000 $6,000Theater $6,000 $6,000 $5,000 A. Which option should the real estate investor choose if he uses the LaPlace criterion? B. Using a…arrow_forward
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