Linear programming:Primal and Dual problem
(a) Following is the Primal problem: Primal Problem: Maximize Total profit Z=120x1+40x2+60x3 S.t x1+x2+x3<=100(No of acres) $400x1+$160x2+$280x3<=$20000(cost per acres) Example is attached.
(a) Following is the Primal problem: Primal Problem: Maximize Total profit Z=120x1+40x2+60x3 S.t x1+x2+x3<=100(No of acres) $400x1+$160x2+$280x3<=$20000(cost per acres) Example is attached.
A logistics specialist for Wiethoff Inc. must distribute cases of parts from 3 factories to 3 assembly plants. The monthly supplies and demands, along with the per-case transportation costs are: Destination Assembly Plant 1 2 3 Supply Source A 5 9 16 200 Factory B 1 2 6 400 C 2 8 7 200 Demand 120 620 60 What are the
Formulate and solve the following problem. Use method of your choice. The Marketing Club at your college has decided to raise funds by selling three types of T-shirts: one with single-color "ordinary" design, one with a two-color "fancy" design, and one with a three-color "very fancy" design. The club feels that it can sell u
(#46)Mountain Laurel Vineyards produces three kinds of wine- Mountain Blanc, Mountain Red, and Mountain Blush. The company has 17 tons of grapes available to produce wine this season. A cask of Blanc requires 0.21 tons of grapes, a cask of Red requires 0.24 tons, and a cask of Blush requires 0.18 tons. The vineyard has enough s
A company produces two products, A and B, which have profits of $9 and $7, respectively. Each unit of product must be processed on two assembly lines, where the required production times are as follows. Hours/Unit Product Line 1 Line 2 A 12 4 B 4
29. Alexis Harrington received an inheritance of $95,000, and she is considering two speculative investments the purchase of land and the purchase of cattle. Each investment would be for one year. Under the present (normal) economic conditions, each dollar invested in land will return the principal plus 20% of the principal;ea
Consider the following linear program: Min 2A+2B s.t. 1A+3B≤12 3A+1B≥13 1A-1B=3 A,B≥0 a. Show the feasible region. b. What are the extreme points of the feasible region? c. Find the optimal solution using the graphical solution procedure.
1. Which of the following mathematical relationships could be found in a linear programming model? And which could not (why)? a. -1A + 2B ≤ 70 b. 2A - 2B = 50 c. 1A - 2B^2 ≤ 10 d. 3 √ A + 2B ≥ 15 e. 1A + 1B = 6 f. 2A + 5B + 1AB ≤ 25 2. Find the solutions t
1. For the linear program: Max 2A + 3B s.t. 1A + 2B ≤ 6 5A + 3B ≤ 15 A,B ≥ 0 Find the optimal solution using the graphical solution procedure. What is the value of the objective function at the optimal solution? 2. Solve the following linear program using the graphical solution procedure.
The lakeside boatwork is planning to manufacture three types of molded fiberglass recreation boats, a fishing (bass0 boat, a ski boat, and a small speedboat. The estimated selling price and variable cost for each type of boat are summarized in the following table Bass $12,500 $23,000 Ski 8,5000 18,000 speed
The Jones Furniture company produces tables and chairs from two resources: labor and wood. The company has 80 hours of labor and 34 pounds of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 pounds of wood to produce, whereas a table requires 10 hours of labor and 7 p
Khan manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Khan needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade A carpet uses 50 units of synthetic fiber, requires 25 hours of production tim
A restaurant sells ice cream and frozen yogurt. The restaurant makes one order for ice cream and frozen yogurt per week, and the store has enough freezer space for 110 gallons of both products. A gallon of froze yogurt costs $0.85 and a gallon of ice cream costs $0.95, and the restaurant budges $90 a week for these products. The
A restaurant sells ice cream and frozen yogurt. The restaurant makes one order for ice cream and frozen yogurt per week, and the store has enough freezer space for 110 gallons of both products. A gallon of froze yogurt costs $0.85 and a gallon of ice cream costs $0.95, and the restaurant budges $90 a week for these products. The
The Smith family owns 405 acres of farmland in Virginia on which they grow corn and tobacco. Each acre of corn costs $110 to plan, cultivate, and harvest; each acre of tobacco costs $215. The Smith family budget $55,000 for next year. The government wants to limit the number of acres of tobacco that can be planted to 100 acres.
Linear Programing Shale-Bituminous Processors Shale Bituminous Processors (SBP) is a medium-sized oil company. Using its own patented process, it produces low- and high-sulphur crude from coal and shale. These oils are used by refiners who process them into products such as gasoline, jet fuel, industrial lubricating oils
Looking for assistance in setting up the problem. I am trying to establish the constraints and the table for solver. (See attached) Transportation System A company which manufactures product in five plants ships locally using its own transportation system, but has orders which must be sent to locations too far to be servi
I have a study problem that I need help with. We're studying network models and linear programming models related to transshipment and transportation. Here is the specific problem I need help with: ----------------------------------------------------------------------- The following table shows the unit shipping co
Solve by Simplex Method: Maximize P=X1 + 2X2 Subject 2X1 + 2X2 ≤ 8 4X1 + 2X2 ≤ 12 -3X1 + 5X2 ≤ 15 X1 ≤ 4 where X1, X2 ≥ 0
Solve the following linear program either by hand using the simplex procedure or by using excel solver. Maximize P = 3X1 + 2X2 Subject to 10X1 + 2X2 ≤ 20 X1 + X2 ≤ 6 where X1, X2 ≥ 0
1. The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: Carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm
In the following exercise, (a.) use the simplex method to solve the problem and (b.) explain what the values of the slack variables in the optimal solution mean in the context of the problem. 1. A manufacturer of bicycles builds one, three, and ten-speed models. The bicycles are made of both aluminum and steel. The company
The exercise is attached. I really was able to understand your work last time.
Max Z = $0.30x + $0.90y Subject to : 2x + 3.2y 160 4x + 2y 240 y 40 x, y Solve for the quantities of x and y which will maximize Z. What is the value of the slack variable associated with constraint 2? Use Lingo10 or QM to solve. Include your solution screen shots
Max 8X + 7Y s.t. 15X + 4Y < 75 10X + 7Y < 70 X + Y < 8 X, Y > 0 a.Use a graph to show each constraint and the feasible region. b.Identify the optimal solution point on your graph.What are the values of X and Y at the optimal solution? c.What is the optim
See also attachment for formatting. 1. Solve the following linear programming model by using the computer: Maximize Z = 5x1 + 8x2 Subject to 3x1 + 5x2 ≤ 50 2x1 + 4x2 ≤ 40 x1 ≤ 8 x2 ≤ 10 x1, x2 ≥ 0 2. Solve the following linear programming model by using the computer:
[See the Attached Questions File.] (1) Graph the following systems of inequalities; find the solution region and the vertices. (2) Solve the following linear programming graphically. ... (5) (a) A nutritionist is designing a new breakfast cereal using wheat germ and enriched oat flour as the basic ingredients. Each ounce of wh
[See the Attached Questions File.] (1) Graph the following systems of inequalities; find the solution region and the vertices. (2) Solve the following linear programming graphically. ... (5) (a) A nutritionist is designing a new breakfast cereal using wheat germ and enriched oat flour as the basic ingredients. Each ounce of wh
How do I set up the problem and find the maximum profit? I have tried for hours but still confused. Linear programming The Grand Strand Oil Company The Grand Strand Oil Company produces regular and premium gasoline for independent service stations in the southeastern United States. The Grand Strand
The Live Wright Medical Supplies Company has a total of 12 salespeople it wants to assign to three regions-the South, the East, and the Midwest. A salesperson in the South earns $600 in profit per month for the company, a salesperson in the East earns $540, and a salesperson in the Midwest earns $375. The southern region can hav