In a typical production scheduling model like Pigskin’s, if there are no production capacity constraints—the company can produce as much asit needs in any time period—but there are storage capacity constraints and demand must be met on time, is it possible that there will be no feasible solutions? Why or why not?
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In a typical production
it needs in any time period—but there are storage capacity constraints and demand must be met on time, is it possible that there will be no feasible solutions? Why or why not?
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- In the Great Threads model, we found an upper bound on production of any clothing type by calculating the amount that could be produced if all of the resources were devoted to this clothing type. a. What if you instead use a very large value such as 1,000,000 for this upper bound? Try it and see whether you get the same optimal solution. b. Explain why any such upper bound is required. Exactly what role does it play in the model?If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor, which of the following constraints reflects this situation? a. 300x1 + 125x2 = 4,000 b. 425(x1 + x2) < 4,000 c. 300x1 + 125x2 > 4,000 d. 300x1 + 125x2 < 4,000You are the finance manager of the firm Sunderland Plastics Limited, which produces two products (X1 and X2) using two different machines (M1 and M2). Each unit of X1 requires 4 hours of processing time on M1 and 2 hours of processing time on M2. Each unit of X2 that gets produced requires a 1 hour processing time on M1 and 1.5-hour processing time on M2.The firm has an available processing time of 40 hours of M1 and 30 hours of M2 available this week. The firm also meets the non-negativity constraints. Your task is the following:The firms makes a net profit of 400 USD from 1 unit of product X1 and 100 USD from 1 unit of product X21) Formulate a linear programming problem in the standard form for Sunderland Plastics Limited.2) Solve the problem graphically and show what combination of the products X1 and X2 the firm should produce to maximise its profit while satisfying the constraints it is facing. How much profit will the firm make?
- In a capital budgeting problem, a decision maker having a limited amount of budget is considering to give financial support to research project A, B, C, D and E. Suppose is a binary variable, which equals 1 if project is chosen and 0 otherwise. Which of the following logical constraints correctly models the requirement that “If Project C is not chosen, Then Projects A and B must be chosen”? A. Xa +Xb <= Xc B. 1- Xc <= Xa +Xb C. 1- Xc <= Xa , 1- Xc <= Xb D. Xa +Xb <= 1 + XcBased on Zangwill (1992). Murray Manufacturing runs a day shift and a night shift. Regardless of the number of units produced, the only production cost during a shift is a setup cost. It costs $8000 to run theday shift and $6000 to run the night shift. Demand for the next two days is as follows: day 1, 4000; night 1, 3000; day 2, 2000; night 2, 5000. It costs $1 per unit to hold a unit in inventory for a shift.a. Determine a production schedule that minimizes the sum of setup and inventory costs. All demand must be met on time. (Note: Not all shifts have to be run.)b. After listening to a seminar on the virtues of the Japanese theory of production, Murray has cut the setup cost of its day shift to $1000 per shift and the setup cost of its night shift to $3500 per shift. Nowdetermine a production schedule that minimizes the sum of setup and inventory costs. All demand must be met on time. Show that the decrease in setup costs has actually raised the average inventorylevel. Is this…Consider a capital budgeting problem with seven projects represented by binary (0 or 1) variables X1, X2, X3, X4, X5, X6, X7. Write a constraint modeling the situation in which only 2 of the projects from 1, 2, 3, and 4 must be selected. Write a constraint modeling the situation in which at least 2 of the project from 1, 3, 4, and 7 must be selected. Write a constraint modeling the situation project 3 or 6 must be selected, but not both. Write a constraint modeling the situation in which at most 4 projects from the 7 can be selected.
- GM manufactures bikini swimming suits. Their business is highly seasonal, with expected demands being 2800, 500, 100, and 850 dozen suits over the four quarters of next year. The company can produce 1200 dozen suits per quarter, but inventories must be built up to meet larger demands at a cost of $15 per dozen per quarter. GM wants to meet demand while minimizing this inventory cost. Formulate a time-phased LP with infinite time horizon. Findthe optimum solution using any solverA company produces A, B, and C and can sell theseproducts in unlimited quantities at the following unit prices:A, $10; B, $56; C, $100. Producing a unit of A requires 1hour of labor; a unit of B, 2 hours of labor plus 2 units ofA; and a unit of C, 3 hours of labor plus 1 unit of B. AnyA that is used to produce B cannot be sold. Similarly, anyB that is used to produce C cannot be sold. A total of 40hours of labor are available. Formulate an LP to maximizethe company’s revenues.Par Inc. manufactures two lightweight Motorcycles, Par-rider and Lady-sport. Par Inc. produces the engines for both models at its Des Moines plant. Each Par-rider engine requires 6 hours of manufacturing time, and each Lady-sport engine requires 3 hours of manufacturing time. The Des Moines plant has 2100 hours of engine manufacturing time available for the next production period. The supplier can only provide up to 300 Lady-sport for the next production period, but there is no limitation for Par-rider engine production. Final assembly and testing require 2 hours for each Par-rider model and 3 hours for each Lady-sport model. A maximum of 1000 hours of assembly and testing time are available for the next production period. The company's accounting department projects a profit contribution of $2400 for each Par-rider produced and $1500 for each Lady-sport produced. Formulate the model to maximize the profit. Solve the problem graphically. What is the optimal solution? Show all your…
- Carlo and Anita make mailboxes and toys in their craft shop near Lincoln. Each mailbox requires 1 hour of work from Carlo and 1 hourfrom Anita. Each toy requires 1 hour of work from Carlo and 4 hoursfrom Anita. Carlo cannot work more than 6 hours per week and Anita cannot work more than 12 hours per week. If each mailbox sells for $12 and each toy sells for $23, then how many of each should they make to maximize their revenue? What is their maximum revenue? Carlo and Anita should make, x mailboxes and y toys. Their maximum revenue is:A sales representative lives in Bloomington and must bein Indianapolis next Thursday. On each of the days Monday,Tuesday, and Wednesday, he can sell his wares in Indianapolis,Bloomington, or Chicago. From past experience, he believesthat he can earn $12 from spending a day in Indianapolis, $16from spending a day in Bloomington, and $17 from spendinga day in Chicago. Where should he spend the first three daysand nights of the week to maximize his sales income lesstravel costs? Travel costs are shown in Table 2. To From Indianapolis Bloomington ChicagoIndianapolis — 5 2Bloomington 5 — 7Chicago 2 7 —The operations manager of a mail order house purchases double (D) and twin (T) beds for resale. Each double bed costs $500 and requires 100 cubic feet of storage space. Each twin bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each double bed is $300 and for each twin bed is $150. The manager’s goal is to maximize profits.What is the storage space constraint?