A furniture maker makes three different style of wardrobes: x,, x, and x, . The manufactureof each style of wardrobe requires a certain amount of time in three types of skilled labor:cutting, assembling and painting. Model x, requires 1 hour for the cutting of component parts,2 hours for assembling and 4 hours for painting. Model x, requires 2 hours for cutting, 4hours for assembling and painting, respectively. While model x, needs 3, 7 and 5 hours forcutting, assembling and painting accordingly. Currently, 200 cutting hours of componentparts, 300 assembling hours and 150 painting hours are available. Determine the product mixthat will maximize the furniture maker's revenue if a model x, sells for $20, a painted modelx, sells for $30, an unpainted model x, sells for $20 and a model x, sells for $50.(a) Formulate a linear programming model for this problem.(b) Find the optimal solution by using simplex algorithm.

Given: A furniture maker makes three different styles of wardrobes: x1, x2, and x3. The manufacture…

Answered: A furniture maker makes three different…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A manufacturing plant makes two types of inflatable boats: two-person boats and four-person boats. Each two-person boat requires 1 labor-hour from the cutting department and 2 labor- hour from the assembly department. Each four-person boat requires 2 labor-hours from the cutting department and 2 labor-hours from the assembly department. The maximum labor- hours available per month in the cutting department and the assembly department are 600 and 700, respectively. The company makes a profit of $25 on each two-person boat and $40 on each four-person boat. (A) Write the linear programming that maximizes the profit. (B) Solve part (A) graphically.
A population gathers plants and animals for survival. They need at least 440 units f energy, 300 units of protein, and 8 hides. One unit of plants provides 30 units of energy, 10 units of protein, and 0 hides. One animal provides 20 units of energy, 25 units of protein, and 1 hide. Only 26 units of plants and 27 animals are available. It costs 20 hours of labor to gather one unit of a plant and 12 hours for an animal. Find how many units of plants and animals should be gathered to meet the requirements with a minimum number of hours of labor. The population should gather 3 units of plants and 11 animals. (Simplify your answers.)
A company produces three types of bookcases: Standard, Deluxe, and Premium. Each bookcase must be sanded, assembled and painted. The Standard model requires 1 hour to sand, 2 hours to assemble, and 1 hour to paint. The Deluxe model requires 2 hours to sand, 3 hours to assemble and 1 hour to paint. The Premium model requires 1 hour to sand, 4 hours to assemble and 2 hours to paint. There are 170 hours available for sanding, 320 hours for assembling and 130 hours for painting. How many of each product can be made? Solve using cramers rule. a. wriite the system of equations for this information. identify variables b. write and label each of the four determinants, do not evaluate. c. solve for only the first variable in the system. use co-factors and minors to solve the d determinant. label the answer
Infotron Inc makes electronic hockey and soccer games. Each hockey game requires 2 labor-hours of assembly and 2 labor-hours of testing. Each soccer game requires 3 labor-hours of assembly and 1 labor-hour of testing. Each day there are 63 labor-hours available for assembly and 33 labor-hours available for testing. How many of each game should Infotron produce each day to maximize its total daily output?
The 1-Dream company makes two different BLU-ray players, which are assembled on two different assembly lines. Line 1 can assemble 40 units of the BLU-Ray player and 55 units of the BLU-Ray player with DVR per hour, and line 2 can assemble 110 units of the BLU-Ray player and 195 units of the BLU-Ray player with DVR per hour. The company needs to produce at least 3,989 BLU-Ray players and 6,755 BLU-Ray player with DVR to fill an existing order. It cost $100 per hour to run line 1 and $310 per hour to run line 2, how many hours should each line run to fill the order at minimum cost? (Use x for line 1 hours and y for line 2 hours.) Minimize C= ≥ 3,989 6, 755 Enter the solution to the simplex matrix below. If there is no solution enter 'DNE' in the boxes below. If more than one solution exists, enter only one of the multiple solutions below. If needed round hours to 1 decimal place and cost to 2 decimal places. Number of hours to run line 1 is Minimum cost is $ Number of hours to run line 2…
A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 1 unit of protein, 2 units of carbohydrates, and 1 unit of fat. Each ounce of nuts will supply 1 unit of protein, 1 unit of carbohydrates, and 1 unit of fat. Every package must provide at least 8 units of protein, at least 12 units of carbohydrates, and no more than 11 units of fat. Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package. a. Write a system of inequalities to express the conditions of the problem. b. Graph the feasible region of the system. a. Fill in the chart. Protein Carbohydrates Fat Fruit unit(s) per ounce unit(s) per ounce unit(s) per ounce Nuts unit(s) per ounce unit(s) per ounce unit(s) per ounce .. Requirements per package At least At least No more than unit(s) unit(s) unit(s)
The Intellectual Company produces a chemical solution used for cleaning carpets. This chemical is made from amixture of two other chemicals which contain cleaning agent X and cleaning agent Y. Their product must contain175 units of agent X and 150 units of agent Y and weigh at least 100 pounds. Chemical A costs ₱ 8 per pound,while chemical B costs ₱ 6 per pound. Chemical A contains one unit of agent X and three units of agent Y.Chemical B contains seven units of agent X and one unit of agent Y.a. Set up the following: i. Variablesii. Constraintsiii. Objective Functionb. Find the minimum costc. Determine the best combination of the ingredients to minimize the cost.2. The Guinevere Corporation is trying to establish a transportation system of small and large vans. It can spend nomore than ₱ 100,000 for both sizes of vehicles and no more than ₱ 500 per month for maintenance. The Corporation canpurchase a small van, which carries up to 7 passengers, for ₱ 10,000 and maintain it for ₱ 100…
A shoe company manufactures two types of shoes: tennis and basketball. Each shoe requires the use of two operations, stitching and coloring, and there are at most 28 hours available each day for each operation. A pair of tennis shoes requires 2 hours of stitching and 2 hours of coloring, while a pair of basketball shoes needs 1 hour of stitching and 2 hours of coloring. Due to other restrictions, the company can make at most 183 pairs of shoes a day. Additionally, due to a sponsorship agreement, the company needs to produce at least 4 pairs of tennis shoes for each pair of basketball shoes. The objective function is subject to constraints. Determine the constraints below. (Hint: Write the constraints line by line. Separate the non-negativity constraints with commas.)
A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 6 units of protein 4 units of carbohydrates, and 4 unit of fat, and will contain 18 calories. Each K ounce of nuts will supply 3 units of protein, 3 unit of carbohydrate, and 5 units of fat, and will contain 29 calories. Every package must provide at least 6 units of protein, at least 10 units of carbohydrates, and no more than 11 units of fat. What is the least number of calories possible in a package? Write out the inequality for protein using x and y as your variables for ounces of fruit and nuts respectively (Use variables in order) Write out the inequality for carbohydrates using x and y as your variables for ounces of fruit and nuts respectively (Use variables in order) 0 Write out the inequality for fat using x and y as your variables for ounces of fruita my instructor srespectively (Use variables in order)
The firm WebsAreUs creates and maintains Web sites for client companies. There are two types of Web sites: “Hot” sites change their layout frequently but keep their content for long times; “cool” sites keep their layout for a while but frequently change their content. Maintaining a hot site requires 1.5 hours of layout time and 2 hour for content changes. Maintaining a cool site requires 1 hour of layout time and 2 hr for content changes. Everyday WebsAreUs has 12 hrs available for layout changes and 16 hr for content changes on a hot site. Net profit is $50 for a set of changes on a hot site and $250 for a set of changes on a cool site. To maximize profit, how many of each type of site should WebsAreUs maintain daily? How, if at all, do the maximum profit and optimal policy change if the company must maintain at least two hot and 3 cool sites daily?
Bottled water and medical supplies are to be shipped to survivors ofan earthquake by plane. Each container of bottled water will serve 10 people and eachmedical kit will aid 6 people. Each plane can carry no more than 80,000 pounds. The bottledwater weighs 20 pounds per container and each medical kit weighs 10 pounds. Each planecan carry a total volume of supplies that does not exceed 6000 cubic feet. Each waterbottle is 1 cubic foot and each medical kit also has a volume of 1 cubic foot. Thus, the maximum value of z is 36000 and this occurs when x = 0and y = 6000.In practical terms, this means that the maximum number of earthquake survivors whocan be helped with each plane shipment is 36000. This can be accomplished bysending 6000 medical kits.A) TrueB) False
A diet is to contain at least 1596 units of carbohydrates, 2700 units of proteins, and 2568 calories. Two foods are available: F₁ which costs $0.02 per unit and F2, which costs $0.04 per unit. A unit of food F₁ contains 2 units of carbohydrates, 5 units of proteins and 6 calories. A unit of food F₂ contains 8 units of carbohydrates, 5 units of proteins and 4 calories. Find the minimum cost for a diet that consists of a mixture of these two foods and also meets the minimal nutrition requirements. Corner points of the feasible region: If there is more than one corner point, type the points separated by a comma (i.e. (1,2),(3,4)). Minimum cost is: $ when F₁ = and F2 = units units.

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