Problem 3A shipping company is planning on purchasing three different types of boats: A, B and C. Therelevant data is summarized in the following table:Cost (million $) per unitSeating capacityExpected profit ($) per unitA6.5• Required seating capacity: at least 660.• At most 8 type C boats may be purchased45150,000B7.875218,000The objective is to minimize the expansion costs under the following restrictions:• Required returns: $1,800,000.60175,000с9.2• At most 12 boats in all.a. Formulate the linear program that represents this problem and solve it. For thepurposes of this exercise you can assume that is possible to buy fractions of aboat, no need to make the variables integer.b. What is the optimal solution (purchase plan)? How many of each container shouldbe purchased, and what should the resultant cost be?c. Suppose that the requirement of at least 660 for seating capacity is reduced to650. Without resolving the problem, can you determine how this would change theoptimal solution? What would be the new cost?

For this question, I will formulate the Linear programming model, and then, I will solve this LP…

Answered: a. Formulate the linear program that…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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A company possesses two manufacturing plants, each of which can produce three products, X, Y, and Z, from a common raw material. However, the proportion in which the products are produced differs in each plant, and so are plant's operating costs per hour. Data on production per hour and costs are given below, together with current orders in hand of each product. Products Operating cost per hour Y Plant A 4 9. Plant B 4 2 10 Orders on hand 50 24 60 Formulate the above as a linear programming problem. Find the number of production hours needed to fulfill the orders on hand at minimum cost using the using Big M method.
Aa6. please solve with formulas not excell
allons of deionized water from each wholesaler to each distribution center is shown in the following table: Question Viewer a. Which of the following statements regarding setting up the tableau for the optimal solution for this problem is true? B. The sum of supply capacities is greater than the sum of demands, so a dummy distribution center is needed. C. The sum of supply capacities is less than the sum of demands, so a dummy wholesaler is needed. b. What is the total cost of the solution? The optimal cost is $ ((Enter your response rounded to the nearest dollar.)
14
The Tubular Ride Boogie Board Company has manufacturing plants in Tucson, Arizona and Toronto, Ontario. You have been given the job of coordinating distribution of the latest model, the Gladiator, to outlets in Honolulu and Venice Beach. The Tucson plant, when operating at full capacity, can manufacture 620 Gladiator boards per week, while the Toronto plant, beset by labor disputes, can produce only 410 boards per week. The outlet in Honolulu orders 500 Gladiator boards per week, while Venice Beach orders 530 boards per week. Transportation costs are as follows. Tucson to Honolulu: $10 per board; Tucson to Venice Beach: $5 per board. Toronto to Honolulu: $20 per board; Toronto to Venice Beach: $10 per board. (a) Assuming that you wish to fill all orders and ensure full capacity production at both plants, is it possible to meet a total transportation budget of $9,900? O Yes O No If so, how many Gladiator boards are shipped from each manufacturing plant to each distribution outlet? (If…
Problem 20-36 (Algo) Palin's Muffler Shop has one standard muffler that fits a large variety of cars. The shop wishes to establish a periodic review system to manage inventory of this standard muffler. Use the information in the following table to determine the optimal inventory target level (or order-up-to level). Annual demand standard deviation of daily demand Item cost Annual holding cost Review period 2, 240 6 $35.00 20 28 Optimal target level mufflers mufflers per working day per muffler % of item value working days Ordering cost Service probability Lead time Working days $60 per order 89 % 2 working days per year 280 a. What is the optimal target level (order-up-to level)? (Use Excel's NORMSINV() function to find the correct critical value for the given a-level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.)
Allocating too much capacity to a location results in?
John is travelling from home in Sydney to a hotel in Perth. Three stopovers on the way a number of choices of towns for each stop only one hotel to choose from in each town, except for Perth, where there are three hotels (J, K, and L) to choose from Each trip has a different distance resulting in a different cost (petrol) (cost is marked by each arc) Hotels have different costs (cost is marked by each node (town)) ● ● ● The goal is to select a route to and a hotel in Perth so that the overall cost of the trip is minimized. Use dynamic programming (forward recursion) to solve this problem by constructing the usual tables for each stage. Stage: 0 (Sydney) 1 Petrol cost start 22 8 12 Hotel cost 70 80 B 80 25 10 2 50 A E 70 30 10 18 8 7 3 50 F 70 70 H 60 8 10 10 4 (Perth) 50 13 K 10 15 L 60 70
Tokyo Company needs the resources indicate below to produce its products Product Labor (hr./unit) Material (Ib./unit) Profit (S/unit) $3 2. 2. 3. 4. Tokyo Company has a daily labor capacity of 240 available hours and a daily supply of 400 pounds of material. The general linear programming formulation for this problem is as follows maximize 2 3 + Sxy + 2 subject to Sx + 2 + 4xy s 240 4x + Gry + 3y s 400 Management has developed the following set of goals, arranged in order of their importance to the firm (1) Because of recent labor relations difficulties, management wants to avoid underutilization of normal production capacity (2) Management has established a satisfactory profit level of S500 per day (3) Overtime is to be minimized as much as possible (4) Management wants to minimize the purchase of additional materials to avoid handling and storage problems.
An electronics firm is currently manufacturing an item that has a variable cost of $0.50 per unit and a selling price of $1.10 per unit. Fixed costs are $15,000. Current volume is 30,000 units. The firm can substantially improve the product quality by adding a new piece of equipment at an additional fixed cost of $5,600. Variable cost would increase to $0.65 and the selling price would be revised to $1.30 with the expectation that the volume would be 50,000 units as a result of a higher-quality product. If the firm does not add new equipment, its profit will be =_____ dollars (round your response to the nearest whole number and include a minus sign if the profit is negative).
Consider a three-units system presented by the cost function as: C1 = 0.03 P12 + 8.2P1 + 452 C2 = 0.025 P22 + 8.3P2+ 500 C3 = 0.0035 P32 + 7.44P3 + 612 Where P1, P2 and P3 are in MW and the total load demand, PD is 952 (in MW). (a) Compare these three-units system with and without the economic dispatch by drawing the bar graphs for the power of each plants and the total cost in RM/h. (b) Determine the percentage of saving, with and without the optimal economic dispatch. Discuss the answer. (c) Now, P1, P2 and P3 are subjected to the following limits: 50 MW < P1 < 300 MW 100 MW < P2 < 400 MW 100 MW < P3 < 350 MW Compare with the costs in (a). Justify the answer.

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