Operation Research (Upvote will be given. Please write the complete solutions. No long explanation needed.)Please answer letter (a) only 4) In a 3 x 3 transportation problem, let xij be the amount shipped from source ito destination j and let cij be the corresponding transportation cost per unit.The amounts of supply at sources 1, 2, and 3 are 15, 30, and 85 units,respectively, and the demands at destinations 1, 2, and 3 are 20, 30, and 80units, respectively. Assume that the starting northwest-corner solution isoptimal and that the associated values of the multipliers are given us u₁ = -2,U2 = 3, U3 = 5, V₁ = 2, V2 = 5, and v3 = 10.a) Find the associated optimal cost.b) Determine the smallest value of cij for each nonbasic variable that willmaintain the optimality of the northwest-corner solution.

Find the Given details below: Given details: 1 2 3 Supply ui 1 C11 C12 C13 15 -2 2 C21…

Answered: In a 3 x 3 transportation problem, let…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section7.5: Facility Location Models

Problem 24P

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In a 3 x 3 transportation problem, let xij be the amount shipped from source i to destination j and let cij be the corresponding transportation cost per unit. The amounts of supply at sources 1, 2, and 3 are 15, 30, and 85 units, respectively, and the demands at destinations 1, 2, and 3 are 20, 30, and 80 units, respectively. Assume that the starting northwest-corner solution is optimal and that the associated values of the multipliers are given us u1 = -2, u2 = 3, u3 = 5, v1 = 2, v2 = 5, and v3 = 10. a) Find the associated optimal cost. b) Determine the smallest value of cij for each nonbasic variable that will maintain the optimality of the northwest-corner solution.
Consider the following LP problem: Min 6X+ 27Y Subject to : 2 X + 9Y => 25, and X + Y <= 75. Pick a suitable statement for this problem: a. X=37.5, Y=37.5 is the only optimal solution. b. Optimal Obj. function value is 75 c. X = 0, Y = 0 is the only optimal solution. d. Optimal Obj. function value is 0
4. Optimal solutionThe model variables of this model are defined as Xij for i=1,2,3 and j=1,2,3,4. Which represent the amount of grain sent from silo i to mill j. A trucking company ships truckloads of grain from 3 silos to 4 mills. The offers, the demands and the unit costs of transport per load to the different routes are shown in the following table (image). The company wants to ship the trucks on the lowest-cost route.a) Write the value of the basic variables (Xij) that are obtained by applying the northwest corner method and indicate their associated cost (Z). Very important, you only have to match the variable to the value you obtain, for example X14=5, and separate each value of the variable by a comma and space, including, for example, the value of Z=6, which is obtained by evaluating.b) Say if the basic point obtained with the northwest corner method is optimal or not.
3. Objective functionThe model variables of this model are defined as Xij for i=1,2,3 and j=1,2,3,4. Which represent the amount of grain sent from silo i to mill j. A trucking company ships truckloads of grain from 3 silos to 4 mills. The offers, the demands and the unit costs of transport per load to the different routes are shown in the following table (image). The company wants to ship the trucks on the lowest-cost route. a) Write what is the expression of the objective function, based on its variables and costs. You should only write, not write any words alone, Z=expression (in capital letters), since it is a short answer. b) Write only the number that represents how many basic variables the problem has.
Consider the transporatio table below: (a) Use the Northwest-Corner Method, the Least-Cost Method and the VAM to get the starting feasible solution. (b) Find the optimal solution by considering the smalles value of the oibjective function computed in (a).
A company has factories at F1, F2 and F3 which supply to warehouses at W1, W2 and W3. Weekly factory capacities are 200, 160 and 90 units, respectively. Weekly warehouse requiremnet are 180, 120 and 150 units, respectively. Unit shipping costs (in rupess) are as follows: W1 W2 W3 Supply F1 16 20 12 200 F2 14 8 18 160 F3 26 24 16 90 Demand 180 120 150 450 Determine the optimal distribution for this company to minimize total shipping cost.
Consider the following linear programming model: maximize Z = 3x1 + 2x2 subject to : x1 +x2 ≤ 1 x1 + x2 ≥ 2 x1,x2 ≥ 0 a) Write this model in a standard (augmented) form. (i.e. Introduce slack/surplus, artificial etc.)b) Constract the initial simplex tableau and carry on your calculations to solve this model using the simplex method. Interpret your result.
In the transportation model, you determine the lowest number first in the row then in the column & then subtract it to the numbers they are aligned in respectively. *FalseTrueThe transportation model is designed to maximize the total cost of delivering products from a source to a destination. *FalseTrueA goal programming problem had two equally important goals. Goal number 1: to achieve exactly $1,500 profit; Goal number 2: to avoid overtime. The objective function for this goal programming problem is written as: Minimize G = 2(d1-) + (d1+) + (d2+) *FalseTrueSetup cost (dollars per inventory unit per unit time) includes: capital invested in inventory, storage and handling of material, & insurance. *TrueFalsePlacing a new order whenever the inventory level drops to a specific re-order point is known as periodic order. *FalseTrue
The second-largest public utility in the nation is the sole provider of elasticity in 32 counties of southern Florida. To meet the monthly demand for electricity in these counties, which is given by the inverse demand function P = 1,200 – 4Q, the utility company has set two electric generating facilities: Q1 kilowatts are produced at facility 1 and Q2 kilowatts are produced at facility 2 (so Q = Q1 + Q2). The costs of producing electricity at each facility are given by C1(Q1) = 8,000 + 6Q12 and C2(Q2) = 6,000 + 3Q22 , respectively. Determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profits.
Suppose we are solving a maximization problem andthe variable xr is about to leave the basis.a What is the coefficient of xr in the current row 0?b Show that after the current pivot is performed, thecoefficient of xr in row 0 cannot be less than zero.c Explain why a variable that has left the basis on agiven pivot cannot re-enter the basis on the next pivot.
Suppose a company must service customers lying inan area of A sq mi with n warehouses. Kolesar and Blumhave shown that the average distance between a warehouseand a customer is An Assume that it costs the company $60,000 per year tomaintain a warehouse and $400,000 to build a warehouse.(Assume that a $400,000 cost is equivalent to foreverincurring a cost of $40,000 per year.) The company fills160,000 orders per year, and the shipping cost per order is$1 per mile. If the company serves an area of 100 sq mi,then how many warehouses should it have?
Consider the following linear programming problem: Min Z = 50x1 + 60x2 s.t. 6x1 + 5x2 >= 30 8x1+4x2 >= 32 x1,x2 >=0. What is the Z in the optimal point of this problem? a. 200 b. 250 c. 300 d. 350 e. none of the abov

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