Your problem will have exactly two variables (an X1 and an X2) and will incorporate a maximization (either profit or revenue) objective. You will include at least four constraints (not including the X1 ≥ 0 and X2 ≥ 0 [i.e., the “Non-negativity” or “Duh!”] constraints). At least one of these four must be a “≤” constraint, and at least one other must be a “≥” constraint; do not include any “= only” constraints. You must have a unique Optimal Solution Point; i.e., no unboundedness or infeasibility problems and no alternative optimal solutions. You will make up the context, the particular numbers (objective function coefficient values), and the relationships (constraint equations and values) for your problem. Your model should be reasonable, plausible, and thoughtfully derived and explained—but not necessarily an accurate reflection of reality (i.e., you can make up the numbers). Make sure you incorporate all of the topics we have gone over. Of course, it is clearly not good enough to just “mention and briefly define” any of these topics and leave it at that; instead, you need to incorporate each in your paper within the context of your problem/situation. Present and discuss your problem (background, objective, constraints, etc.) in “English” and then supplement that in “Math” (linear programming) language. (This is an extremely important part of your paper, and something that you will have to do a lot when you graduate and start a career). The overwhelming majority of your paper will be written in “English,” with a bit of “Math” language stuff thrown in (as opposed to lots of “Math” language with a bit of “English” thrown in). Draw each constraint equation’s own individual graph. Then draw one “final” graph that includes the feasible region, the optimal objective function line (you need to actually graph it; do not just estimate where it goes!), and the optimal solution point. Perhaps the best way to draw these graphs is using a computer program such as EXCEL. Make sure you incorporate (as discussed above) your objective function, constraints, slack and surplus values, optimal solution, optimal objective function value, sensitivity analysis, range of optimality, range of feasibility, dual prices, shadow prices, reduced costs, and anything else that we have discussed that is relevant to your project’s problem/situation. While much of your work will be narrative, of course you should feel free to draw pictures, construct tables, use (and explain!) math equations and “math language,” etc., as you think appropriate and necessary. Re-stating some or all of your computer output in some other form is certainly ok; in fact, that is a big part of this project.
Your problem will have exactly two variables (an X1 and an X2) and will incorporate a maximization (either profit or revenue) objective. You will include at least four constraints (not including the X...
You’ve been asked to develop a problem that can be used to explain some of the concepts you know to someone who has never heard of linear programming. 1. Formulate a maximization problem such that the following conditions are met (you may not use a problem has appeared on this assignment). Make sure to include all elements of formulation that we have discussed (i.e., objective function, constraints, non-negatives). a. LP problem with two decision variables (using X and Y as...
Problem 1 (10 pts): Construct a mathematical model (define your variables, write an objective function and constraints). Problem 2 (10 pts): Use Excel's Solver tool to determine the optimal solution that will maximize profit. Summarize your results. In the Solver toolbox, choose "Simplex LP". Problem 3 (10 pts): Discuss the effect on the optimal solution in Problem 2 if the profit on a small table increases to $12. In the Solver toolbox, rchoose "Simplex LP". If you Copy/Paste from Problem...
Suppose you have a total income of I to spend on two goods x1 and x2, with unit prices p1 and p2 respectively. Your taste can be represented by the utility function u left parenthesis x subscript 1 comma x subscript 2 right parenthesis equals x subscript 1 cubed x subscript 2 squared (a) What is your optimal choice for x1 and x2 (as functions of p1 and p2 and I) ? Use the Lagrange Method. (b) Given prices p1...
could you please solve problem 1 ? Thank you for your cooperation Review Homework.pdf - Adobe Acrobat Pro DC File Edit View Window Help Home Tools. Review Homework.... * 1. Consider the following LP: Max z = 5x1 + x2 s.t. 2x1 + x2 56 Xi - X2 SO 6x1 + x2 S12 X1, X220 Plot the constraints on the graph and identify the feasible region and determine the optimal value of the objective function and the values of the...
Assume that you have exactly 100 hours of labor to allocate between producing goods X and Y. Your output of X and Y depends solely on the hours of labor you spend so the production functions, qi=fLifor i=X and Y, are: X=LX.5 and Y=LY.5 If you can sell your output of X and Y at the fixed prices PX = 10 and PY = 5, how much of goods X and Y would you produce to maximize your income? (Hint:...
1. Consider the following LP: Max z 5x1 X2 st. 2x1 xS6 6x1X2S 12 Plot the constraints on the graph and identify the feasible region and determine the optimal value of the objective function and the values of the decision variables. 2. Priceler manufactures sedans and wagons. The number of vehides that can be sold each of the next three months are listed to Table 1. Each sedan sells for $10000 and each wagon sells for $11000. It cost $7000...
Answer the problem 2 only please. Also if you could upload the excel sheet as well will be very appreciated. thanks OPR 3450 - Fall 2019 Assignment 1 due 09/09/19 page 1 of 1 Assignment 1 This is due in class on multiple dates. Check each Part. Each person must submit his/her own answer. If anyone submits a copy of an assignment, everyone with that submission will get a zero on the assignment. I will not accept e-mail assignments. Each...
Recursion and Trees Application – Building a Word Index Make sure you have read and understood · lesson modules week 10 and 11 · chapters 9 and 10 of our text · module - Lab Homework Requirements before submitting this assignment. Hand in only one program, please. Background: In many applications, the composition of a collection of data items changes over time. Not only are new data items added and existing ones removed, but data items may be duplicated. A list data structure...