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# Linear Programming

### Mathematics - Linear Operators...

Given the following linear programming problem: Min Z = 2x + 8y Subject to (1) 8x + 4y 64 (2) 2x + 4y 32 (3) y 2 At the optimal solution the minimum cost is: a. \$30 b. \$40 c. \$50 d. \$52 d. \$53.33

### Linear Programming : Finding the Lowest Cost Using a Graphing Method

A cook is puzzling over the number of pounds of food he should purchase in order to minimize his cost. He has always bought his food from a small health food store in town. The store sells two types of mixtures. Both of these mixtures contain the three ingredients needed, but the cook needs his own special ratio of these ingredi

### Integer Programming Model : Four Problems to Solve Using a Computer

Please see the attached file for the fully formatted problems. 19. The Avalon Floor Cleaner Company as trying to determine the number of salespeople it should allocate to its three regions-the East, the Midwest, arid the West The company has 100 salespeople that it wants to assign tn the three regions. The annual average un

### Machines Used to Produce Less Cost

Each machine at a certain factory can produce 50 units per hour. The setup cost is \$80 per machine, and the operating cost is \$5 per hour. How many machines should be used to produce 8,000 units at the least possible cost? (Remember that the answer should be a whole number.)

### Linear programming and solve model by using the computer.

Green Valley Mills produces carpet at plants in St Louis and Richmond. The plants ship the carpet to two outlets in Chicago and Atlanta. The cost per ton of shipping carpet from each of the two plants to the two warehoused is as follows: From Chicago Atlanta St Louis \$40 \$65 Richmond \$70

### Linear programming and solve model by using the computer.

The Donnor meat processing firm produces wieners from four ingredients: chicken, beef, pork, and a cereal additive. The firm produces three types of wieners: regualr beef, and all-meat. The company has the following amounts of each ingredient available on a daily basis: Chicken 200 \$.20 Beef 300

The Midland Tool Shop has four heavy presses it uses to stamp out prefabricated metal covers and housings for electronic consumer products. All four presses operate differently and are of different sizes. Currently the firm has a contract to produce three products. The contract calls for 400 units of product 1; 570 units of p

### Linear Programming: Formulate Variables, Objectives and Constraints

How is this problem worked and what are the steps? Problem: Cauchy Canners produces canned whole tomatoes and tomato sauce. This season, the company has available 3,000,000 kg of tomatoes for these two products. To meet the demands of regular customers, it must produce at least 80,000 kg of sauce and 800,000 kg of whole tom

### 3 Linear Program Problems

I need help on how to solve the programming problems below. 1. Solve the following integer programming problem. Provide only the values for A, B, and the Z. You may use any method you choose (graphical, enumeration of vertices, MS Solver, etc.) Maximize Z = 120A + 80B Subject to the constraints: 2A + 1B <= 6 7A +

### Linear Programming : Optimal Profit

The production manager for the Whoppy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. The company operates one "8 hour" shift per day. Therefore, the production time is 480 minutes per day. During the production process, one of the main ingredients, syrup is limited to maximum produ

### Linear Programming : Maximizing Profit and Optimal Values

7. The linear programming problem whose output follows is used to determine how many bottles of fire red nail polish (x1), bright red nail polish (x 2), basil green nail polish(x 3), and basic pink nail polish(x 4) a beauty salon should stock. The objective function measures profit; it is assumed that every piece stocked will be

### Linear Programmng : Product Mix and Total Profit

Mallory Furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs \$500 and requires 100 cubic feet of storage space, and each medium shelf costs \$300 and requires 90 cubic feet of storage space. The company has \$75000 to invest in shelves this week, and the warehouse has 18000 cubic feet

### Linear Programming : Objective Function

4. The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. He can get at most 4800 oz of malt per week and 3200 oz of wheat per week. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of m

### Linear programming : Sensitivity Range

TRUE/FALSE The sensitivity range for an objective coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal.

### Linear Programming : Finding Constraints

A manufacturer buys peas for vegetable pies from 2 cooperatives. The price per unit is \$6 from cooperative A, and \$5.50 per unit from cooperative B. The manufacturer needs at least 12000 units of peas. Cooperative A can supply up to 8000 units, and cooperative B can supply at least 6000 units. Develop constraints for these condi

### Linear Programming Using Excel Solver

I need the following two attached problems done in excel using the built in excel solver. For these problems we need to formulate our own constraints. For some reason I am getting negative numbers, which is obviously not right. I would appreciate it if someone could formulate the right constraints and solve these problems 100% c

### Hoke's Spokes bike shop

Hoke owns Hoke's Spokes bike shop. Bikes are customer orders and stocks bikes for walk in customers. He stocks three types of bikes, road-racing, cross-country, and mountain. A road-racing bike cost 1200, a cross country bike cost 1700, and mountain bike cost 900. He sells road racing bikes for 1800, cross country bikes for

### Linear programming model

Chemco produces a chemical mixture for a specific customer in 1000 pound batches. The mixture contains three ingrediants zinc, mercury, and potassium. The mixture must conform to formula specifications that are supplied by the customer. The company wants to know the amount of each ingredient it needs to put in the mixture tha

### Linear programming and graphically ...

Irwin produces two types of cotton cloth-demin corduroy. Corduroy is a heavy grade of cotton cloth and requires 7.5 pounds of raw cotton per yard, whereas demin requires 5 pounds of raw cotton per yard. A yard of corduroy requires 3.2 hours of processing timel a yard of denim requires 3 hours. Although the demand for denim is

### Mathematics - Finite Mathematics..

Please show all work. Use the Simplex Method to solve the following linear programming problem. Show all tableaus and make a notation of all row operations performed. Maximize: P = 2x1 + 8x2 + 10x3 + x4 subject to the constraints x1 + 2x2 + x3 + x4 <= 50 3x1 + x2 + 2x3 + x4 <= 100 x1 >=0 x2 >= 0 x3 >= 0 x4

### Linear Programming : Finding an Optimal Solution using Excel Solver

Formulate the LP model for the problems below in EXCEL using problem solver: 1. The Big Bang explosives company produces customized blasting compounds for use in the mining industry. The four ingredients for these explosives are agents A, B, C and D. Big Bang just received an order for 2000 pounds of explosive. Agents A and

### Linear programming

See attachment 1. Critical Path Analysis (20%) The planning of projects can often be represented by a network where the arcs of the network represent activities occupying a duration of time and nodes represent the termination and beginning of activities. Two questions can be asked a. What long will it take to complete the

### Graphical Analysis

The bakery makes cakes and pastries in a big pan. the main ingredients are flour and sugar. There are 25 pounds of flour and 16 pounds of sugar available, and the demand for cakes is 5. Five pounds of flour and 2 pounds of sugar are required to make a pan of cakes , and 5 pounds of flour and 4 pounds of sugar are required to

### Linear programming graphically

Please help graph the following linear programming model graphically maximize z= 5x + 8y subj to 3x + 5y <= 50 2x + 4y <= 40 x <=8 y <=10 x ,y >= 0 I am confused at how to graph this. Please help and explain. I do n

### Linear Programming : Graphical Analysis

Please help with solving this problem in graphical analysis and formulate a linear programming model for the below: A company produces two prducts that are processed on two assembly lines. Assembly line 1 has 100 available hours, and assemoly line 2 has 42 available hours. Each prduct equires 10 hours of processing time on l

### Linear Programming

8. Consider the following minimization problem. Min z = x1 + 2x2 s.t. x1 + x2 300 2x1 + x2 400 2x1 + 5x2 750 x1, x2 0 Which constraints are satisfied at the optimal solution (x1 = 250, x2 = 50)? 9. Consider the following minimization problem. Min z = 1.5x1 + 2x2 s.t. x1 + x2 300 2x1 + x2

### Linear programming : Quantitative Methods for Business

All I need is for someone to show me how to put this linear programming problem in standard form. Solution not necessary. (e.g., Max 30x1 + 50x2 +20x3 etc...) with the constraints. Thank you! See attachment for table and full problem. Better Products Inc. manufactures three products on two machines. In a typical week, 40

### Simplex Tableau and Method

1.Introduce slack variables and set up the initial simplex tableau. Do not solve. (See attachment). 2. Determine whatever the given simplex tableau is in final form. If so, found the solution to the associated regular linear programming problem. If not find the pivot element to be used in the iteration of the simplex meth

### Solving linear programming problems using the Simplex Method Please see the attached file for the fully formatted problem(s).

Please see the attached file for the fully formatted problem(s). Determine the maximum value of subject to the constraints show all of the steps of the simplex method. State all solutions, including the maximum value after you have the final tableau. Homework problem 2 A landscape supply company packages three diffe

### Two-phase simplex algorithm

1. Consider the following linear program. Minimize z = -7x1 + 3x2 subject to 2x1 + 4x2 = 15 (C1) - 2x1 + x2 &#8805; 4 (C2) Solve the problem using the two-phase Simplex algorithm as follows. 1) (5%) Write the problem in the equality form 2) (5%) Introduce artificial variables, write the objective of Phase I 3)