the constra given below, WHI 14x X x = 2, y = 1 + + x = 1, y = 2 = 2, y = 5 x x = 5, y = 5 x = 0, y = 4 6y 3y 2 42 26 point is the feasible solutio space of this inimization problem?
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- Please show how to solve bb) The Scott Tractor Company ships tractor parts from Omaha to St. Louis by railroad. However, a contract limits the number of railroad cars the company can secure on each branch/arc during a week. Given these limiting conditions, the company wants to know the maximum number of railroad cars containing tractor parts that can be shipped from Omaha to St. Louis during a week. Phoenix Des Moines 3 5 6. 6. 1. Dallas 2 Omaha St. Louis 7. 3 Denver 6. ActivateW O 31°CA retail store in Des Moines, Iowa, receives shipments of a particular product from KansasCity and Minneapolis. Let x 5 number of units of the product received from Kansas City y 5 number of units of the product received from Minneapolisa. Write an expression for the total number of units of the product received by the retail store in Des Moines. b. Shipments from Kansas City cost $0.20 per unit, and shipments from Minneapolis cost$0.25 per unit. Develop an objective function representing the total cost of shipments to Des Moines. c. Assuming the monthly demand at the retail store is 5000 units, develop a constraint that requires 5000 units to be shipped to Des Moines. d. No more than 4000 units can be shipped from Kansas City, and no more than 3000 units can be shipped from Minneapolis in a month. Develop constraints to model this situation. e. Of course, negative amounts cannot be shipped. Combine the objective function and constraints developed to state a mathematical model…
- Facility Location. A paper products manufacturer has enough capital to build and manage some additional manufacturing plants in the United States in order to meet increased demand in three cities: New York City, NY; Los Angeles, CA; and Topeka, KS. The company is considering building in Denver, CO; Seattle, WA; and St. Louis, MO. Max Operating Capacity 400 tons/day 700 tons/day Denver Seattle $10/ton $17/tor $5/ton $11/ton.... $18/ton.... $28/ton Los Angeles Topeka New York City Figure 1: Graphical representation of the given data = • The cost fi of building plants in these cities is fi $10,000,000 in Seattle. Unmet Demand 300 tons/day 100 tons/day 500 tons/day • Due to geographic constraints, plants in Denver and Seattle would have a maximum operating capacity kį of 400 tons/day and 700 tons/day respectively. $5,000,000 in Denver and f2 = • The cost cij per ton of transporting paper from city i to city j is outlined in Figure 1. • The unmet demand d, for Los Angeles, Topeka, and New…HMO has 40 doctors to be apportioned among four clinics. The HMO decides to apportion the doctors based on the average weekly patient load for each clinic, given in the following table. Clinic A B C D Average Weekly 275 392 611 724 Patient Load Find the apportion of A and C using using Adam's Method. Use modified divisor 52. Doctors for clinic A Doctors for clinic B = %3D Doctors for clinic C= Doctors for clinic D =Show that any 2 *2 matrix A that does not have aninverse will have det A= 0.
- For the remaining questions, consider the following problem description: An oil company is considering exploring new well sites S₁, S2, ..., S10 with respective costs C1, C2, C10. And in particular they want to find the least-cost selection of 5 out of the 10 possible sites. The binary decision variables x₁,x2,..., X10 denote the decision to explore the corresponding site.Solve the following Linear Programming model using the graphical method (USING EXCEL){Write the steps of construction} Q1)MaximizeH = x + 3y Objective functionsubject tox + y ≤ 502x + y ≤ 60 x ≥ 0, y ≥ 0show the complete solution for a, b and c
- 4. Optimal Rental Decisions in Cloud Computing Assume that AWS has the following 3 options for renting servers. Fraction of Job in one Server Description Rental Low Power Medium Power High Power $2/hr. $4/hr. $9/hr. Hour 1/8 1/6 1/3 L M Note that if you rent a server for less than one hour, you still must pay the rent for the entire hour. You have a job that must finısh in at most 5 hours. The low-power server can finish 1/8th of the job in 1 hour, the medium-power server can finish 1/6 of the job in one hour, and the high- power server can finish 1/3rd of the job in one hour. (a) The typical practice used by most firms is to find a single server that can do the work at the least cost and within the available time. Find the best sıngle server solution-that is, which single server should you use and for how many hours will you rent this server?Four qualified postgraduate students are to be allocated to four professors. The preference given by student (scale 1-10) is shown as table below. Student A В C D Professor James Jordan Janet 7 8 6. Jessy 5 8. 7 (a) Formulate a linear programming model for the problem. [NOTE: Please use x, where i = 1, 2,...,n -Professor and j=1, 2,...,m -Student to represent your decision variables.] (b) From the output below, what is the optimal allocation plan and what is the total preference scales obtained from the allocation plan? Model Variable Original Value Final Value Value x11 1 1 Value x12 1 Value x13 1 Value x14 Value x21 Value x22 Value x23 1 1 1 1 1 Value x24 1 Value x31 Value x32 Value x33 1 1 1 1 Value x34 1 Value x41 1 Value x42 1 Value x43 1 Value x44 1 1 699 445Solve the linear programming problem by the method of corners. Maximize P= x + 6y subject to x + y s4 2x + y s6 x 2 0, y 20 The maximum is P = at (x, y) = Need Help? Read It