PLEASE ANSWER TRUE OR FALSE FOR THE FOLLOWING STATEMENTS:1. To develop an LP mathematical model for a transportation or transshipmentproblem, you must define a variable for each arc and a constraint for each node.2. A transportation problem with 3 sources and 4 destinations will have 12 variablesin the objective function.3. A dummy origin in a transportation problem is used when demand is less thansupply.4. Generally, the optimal solution to an integer linear program is NOT sensitive tothe constraint coefficients than is a linear program.5. The constraint x1-x2= 0 implies that if project 1 is selected, project 2 cannot be.6. If Project 5 must be completed before Project 6, the constraint would be x5 =>x6.

Here, the first three questions are related to transportation problems. The main objective would be…

Answered: 1. To develop an LP mathematical model…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section: Chapter Questions

Problem 34P

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Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?
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%.
Please
Create spreadsheets and use Solver to determine the correct volumes to be produced to minimize cost for the following problem. Your company has two trucks that it wishes to use on a specific contract. One is a new truck the company is making payments on, and one is an old truck that is fully paid for. The new truck’s costs per mile are as follows: 54₵ (fuel/additives), 24₵ (truck payments), 36₵ (driver), 12₵ (repairs), and 1₵ (misc.). The old truck’s costs are 60₵ (fuel/additives), 0₵ (truck payments), 32₵ (rookie driver), 24₵ (repairs), and 1₵ (misc.). The company knows that truck breakdowns lose customers, so it has capped estimated repair costs at $14,000. The total distance involved is 90,000 miles (to be divided between the two trucks).
given the transportation problem, assume that the demands at the 4 destinations are 5, 5, 7, and 8 units, respectively, and the supplies at the 4 sources are 7, 3, 7 and 8 units, respectively.C₁₁=7ㅤ C₁₂=9ㅤ C₁₃ = 1ㅤ C₁₄ = 10 C₂₁= 22ㅤ C₂₂ = 25ㅤ C₂₃ = 16ㅤ C₂₄ = 26 С₃₁ = 28ㅤ C₃₂ = 32ㅤ C₃₃ = 24ㅤ Сз₄ = 32 C₄₁ = 12ㅤ C₄₂ = 14ㅤ C₄з = 6ㅤ C₄₄ = 16where m=4, n=4what is the optimal solution using vogel's approximation method, least-cost method, and northwest-corner rule?
eBook Problem 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: Room Type 1 Type II Rental Class Super Saver $37 $18 Explain. Deluxe $40 $33 Variable SuperSaver rentals allocated to room type I SuperSaver rentals allocated to room type II Deluxe rentals allocated to room type I Deluxe rentals allocated to room type II Business rentals allocated to room type II Is the demand by any rental class not satisfied? Business Type 1 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 125 rentals in the Super Saver…
1. If constraint has a shadow price of $6, Right-Hand-Side (RHS) is 12, allowable increase is 2, allowable decrease is 4. How would objective function change if the RHS of this constrains changes from 12 to 9? Answer___________
Assuming that the company is interested in maximizing the total profit contribution, answer the following: A, What is the linear programming model for this problem? Decision Variables: LP Model: B.Find the optimal solution using the graphical solution procedure. 1.Feasible Region:2. Identify the binding constraint/s:3. Identify the rebundant constraint/s:4.How many gloves of each model should Kelson manufacture?5.What is the total profit contribution Kelson can earn with the given production quantities? C.How many hours of production time will be scheduled in each department? D.What is the slack time in each department? E.Compute the range of optimality for the objective function coefficients
A transport company engaged in carying parcels has three branches to serve five customers. This distance (km) from each branch to each of the customers is given below: Branches Customers Number of C trucks available I 10 12 6. 15 II 4. 4. 6. 6. 7. 12 III 15 7. 11 13 8. 16 Number of 4. 6. trucks required i. Find out using Vogel's Approximation Method (VAM) the allocation of trucks from branches to customers in order to minimize the total cost of transportation assuming that the cost is proportional to distance. What is the minimum required distance (km) to be run by the trucks? i. If an amival of a V.V.I.P. blocks the traffic from branch II to customers D and E, what should be the optimal allocation in order to minimize the total transportation cost? 111. 8.
Explain how to determine the number of variables and constraints that would be in a transportation problem simplyby knowing the number of sources and the number of destinations.
fertilizer manufacturer has to fulfill supply contracts to its two main customers (650 tons to Customer A and 800 tons to Customer B). It can meet this demand by shipping existing inventory from any of its three warehouses. Warehouse 1 (W1) has 400 tons of inventory onhand, Warehouse 2 (W2) has 500 tons, and Warehouse 3 (W3) has 600 tons. The company would like to arrange the shipping for the lowest cost possible, where the per-ton transit costs are as follows: W 1 W 2 W 3 Customer A $7.50 $6.25 $6.50 Customer B $6.75 $7.00 $8.00 Write the objective function and the constraint in equations. Let Vij= tons shipped to customer i from warehouse j, and so on. For example, VA1=tons shipped to customer A from warehouse W1. This exercise contains only parts b, c, d, e, and f. Part 2 b) The objective function for the LP model =

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