Please answer letter B and show your solution. 8:19 - O OAsynchronomus 1_Linear Programming.docxoptain a maximum saie ?Problem BClarita has an online shop where she sells hand-made paintings and cards. She sells the painting for $50 andthe card for $20. It takes her 2 hours to complete 1 painting and 45 minutes to make a single card. She also hasa day job and makes paintings and cards in her free time. She cannot spend more than 15 hours a week tomake paintings and cards. Additionally, she should make not more than 10 paintings and cards per week.She makes a profit of $25 on painting and $15 on each card. How many paintings and cards should she makeeach week to maximize her profit.Problem CAt the Institute, Professor- X wishes to employ two people, Juanito and Maria, to grade papers for his classes.Juanito is a graduate student and can grade 20 papers per hour; Juanito earns $15 per hour for grading papers.Maria is a post-doctoral associate and can grade 30 papers per hour; Maria earns $25 per hour for gradingpapers. Each must be employed at least one hour a week to justify their employment.If Prof-X has at least 110 papers to be graded each week, how many hours per week should he employ eachperson to minimize the cost?Problem DColonel Alexander Hamilton is on a low cholesterol diet. During lunch at the HQ cafeteria, he always choosesbetween two meals, Pasta or Tofu.The table below lists the amount of protein, carbohydrates, and vitamins each meal provides along with the

Here clarita can work for 15 hours a week only and she takes 2hour for 1 painting to complete and 45…

Answered: Problem B Clarita has an online shop…

Understanding Business

12th Edition

ISBN:9781259929434

Author:William Nickels

Publisher:William Nickels

Chapter1: Taking Risks And Making Profits Within The Dynamic Business Environment

Section: Chapter Questions

Problem 1CE

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Although the problems say solve graphically, please solve all problems using the QM for Windows software or solve manually. B.6 The Christina Alvarez Company manufactures two lines of designer yard gates, called model A and model B. Every gate requires blending a certain amount of steel and zinc, the company has available a total of 25.000 Ib of steel and 6,000 lb of zinc. Each model A gate requires a mixture of 125 Ib of steel and 20 lb of zinc, and each yields a profit of 590. Each model B gate requires 100 1b of steel and 30 ib of zinc and can be sold for a profit of $70. Find by graphical IP the best production mix of yard gates.
Ana is a university student with 12 hours available daily, and she wants to distribute her time betweenstudy (x) and leisure (y) activities. She wants to maximize her total enjoyment while fulfilling heruniversity obligations. Ana considers leisure to be twice (2) as enjoyable as studying, but she alsobelieves that she should spend at least twice (2) as much time studying as she does on leisure activities.Additionally, she cannot spend more than five (5) hours a day on leisure activities to ensure that she hasenough time for her university obligations. 1. How much additional enjoyment would Ana get if she had one more hour per dayavailable, so 13 instead of 12 (dual price)?2. Would Ana experience a greater level of enjoyment if she allows herself to have amaximum of six hours per day to leisure activities instead of five, while still fulfilling her universityobligations within the 12 hours available (dual price)?3. What is the allowable increase of the coefficient accompanying leisure…
Sunseel Industries produces two types of raw materials, A and B, with a production cost of $4 and $8 per unit, respectively. The combined production of A and B must be at least 700 units per month. The factory is expected to produce at least 400 units of B and not more than 1200 units of A each month. The processing times for A and B are observed to be 5 hours and 4 hours, respectively. A total of 3000 production hours are available per month. Develop a linear program that Sunseel Industries can use to determine the number of units of each raw material to produce that will meet the demand and minimize the total cost.
Tiny Toy Company makes three types of new toys: the tiny tank, the tiny truck, and the tiny turtle. Plastic used in one unit of each is 1.5, 2.0 and 1.0 pounds, respectively. Rubber for one unit of each toy is 0.5, 0.5, and 1.0 pounds, respectively. Also, each tank uses 0.3 pounds of metal, and the truck uses 0.6 pounds of metal during production. The average weekly availability for plastic is 16,000 pounds, 9,000 pounds of metal, and 5,000 pounds of rubber. It takes two hours of labor to make one tank, two hours for one truck, and one hour for a turtle. The company allows no more than 40 hours a week for production (priority #1). Finally, the cost of manufacturing one tank is $7, 1 truck is $5 and 1 turtle is $4; a target budget of $164,000 is initially used as a guideline for the company to follow. Minimize over-utilization of the weekly available supply of materials used in making the toys and place twice as much emphasis on the plastic (priority #2) I understand…
A toy manufacturer preparing a production schedule for two new toys, trucks spinning tops,must use the information concerning their construction times below.Machine A Machine B FinishTruck 2hr 3hr 5hrSpinning Top 1hr 1hr 1hrFor example, each truck requires 2 hours on machine A. The available employee hours per weekare as follows: For operating machine A; 80 hours; for B, 50 hours; for finishing 70 hours. If theprofits on each truck and spinning top are R7 and R2, respectively, how many of each toyshould be made per week to maximize profit? What is the maximum profit?
what is the dual equivalent and the final tableau of the given primal linear programming model?Min Y₀ = 10Y₁ + 8Y₂s.t.Y₁ + 2Y₂ ≥ 52Y₁ - Y₂ ≥ 12Y₁ + 3Y₂ ≥ 4Y₁ ≥ 0, Y₂ is unrestrictedprove or disprove the complementary slackness theorem.
The Tiny Toy Company makes three types of new toys: the tiny tank, the tiny truck, and the tiny turtle. Plastic used in one unit of each is 1.5, 2.0 and 1.0 pounds, respectively. Rubber for one unit of each toy is 0.5, 0.5, and 1.0 pounds, respectively. Also, each tank uses 0.3 pounds of metal, and the truck uses 0.6 pounds of metal during production. The average weekly availability for plastic is 16,000 pounds, 9,000 pounds of metal, and 5,000 pounds of rubber. It takes two hours of labor to make one tank, two hours for one truck, and one hour for a turtle. The company allows no more than 40 hours a week for production (priority #1). Finally, the cost of manufacturing one tank is $7, 1 truck is $5 and 1 turtle is $4; a target budget of $164,000 is initially used as a guideline for the company to follow. a) Minimize over-utilization of the weekly available supply of materials used in making the toys and place twice as much emphasis on the plastic (priority #2) b) Minimize the…
A garden store prepares various grades of pine bark for mulch: nuggets (x1), mini-nuggets (x2),and chips (x3). The process requires pine bark, machine time, labor time, and storage space. Thefollowing model has been developed.Maximize Z = 9 x1 + 9x2 + 6x3 (profit)Subject toBark 5x1 + 6x2 + 3x3 ≤ 600 pounds Machine 2x1 + 4x2 + 5x3 ≤ 600 minutesLabor 2x1 + 4x2 + 3x3 ≤ 480 hoursStorage 1x1 + 1x2 + 1x3 ≤ 150 bags x1, x2, x3 ≥ 0 a. What is the marginal value of a pound of pine bark? Over what range is this price valueappropriate?b. What is the maximum price the store would be justified in paying for additional pine bark?c. What is the marginal value of labor? Over what range is this value in effect?d. The manager obtained additional machine time through better scheduling. How much additional machine time can be effectively used for this operation? Why?e. If the manager can obtain either additional pine bark or additional storage space, which oneshould she choose and how much (assuming…
A garden store prepares various grades of pine bark for mulch: nuggets (x1), mini-nuggets (x2),and chips (x3). The process requires pine bark, machine time, labor time, and storage space. Thefollowing model has been developed.Maximize Z = 9 x1 + 9x2 + 6x3 (profit)Subject toBark 5x1 + 6x2 + 3x3 ≤ 600 pounds Machine 2x1 + 4x2 + 5x3 ≤ 600 minutesLabor 2x1 + 4x2 + 3x3 ≤ 480 hoursStorage 1x1 + 1x2 + 1x3 ≤ 150 bags x1, x2, x3 ≥ 0 a. What is the marginal value of a pound of pine bark? Over what range is this price valueappropriate?
The Tiny Toy Company makes three types of new toys: the tiny tank, the tiny truck, and the tiny turtle. Plastic used in one unit of each is 1.5, 2.0 and 1.0 pounds, respectively. Rubber for one unit of each toy is 0.5, 0.5, and 1.0 pounds, respectively. Also, each tank uses 0.3 pounds of metal and the truck uses 0.6 pounds of metal during production. The average weekly availability for plastic is 16,000 pounds, 9,000 pounds of metal, and 5,000 pounds of rubber. It takes two hours of labor to make one tank, two hours for one truck, and one hour for a turtle. The company allows no more than 40 hours a week for production (priority #1). Finally, the cost of manufacturing one tank is $7, 1 truck is $5 and 1 turtle is $4; a target budget of $164,000 is initially used as a guideline for the company to follow. Minimize over-utilization of the weekly available supply of materials used in making the toys and place twice as much emphasis on the plastic (priority #2) Minimize the under and…
The Tiny Toy Company makes three types of new toys: the tiny tank, the tiny truck, and the tiny turtle. Plastic used in one unit of each is 1.5, 2.0 and 1.0 pounds, respectively. Rubber for one unit of each toy is 0.5, 0.5, and 1.0 pounds, respectively. Also, each tank uses 0.3 pounds of metal and the truck uses 0.6 pounds of metal during production. The average weekly availability for plastic is 16,000 pounds, 9,000 pounds of metal, and 5,000 pounds of rubber. It takes two hours of labor to make one tank, two hours for one truck, and one hour for a turtle. The company allows no more than 40 hours a week for production (priority #1). Finally, the cost of manufacturing one tank is $7, 1 truck is $5 and 1 turtle is $4; a target budget of $164,000 is initially used as a guideline for the company to follow. a) Minimize over-utilization of the weekly available supply of materials used in making the toys and place twice as much emphasis on the plastic (priority #2) b) Minimize the under…
Weenies and Buns is a food processing plant which manufactures hot dogs and hot dog buns. They grind their own flour forthe hot dog buns at a maximum rate of 200 pounds per week. Eachhot dog bun requires 0.1 pound of flour. They currently have a contract with Pigland, Inc., which specifies that a delivery of 800pounds of pork product is delivered every Monday. Each hot dogrequires pound of pork product. All the other ingredients in thehot dogs and hot dog buns are in plentiful supply. Finally, the laborforce at Weenies and Buns consists of 5 employees working fulltime (40 hours per week each). Each hot dog requires 3 minutes oflabor, and each hot dog bun requires 2 minutes of labor. Each hotdog yields a profit of $0.80, and each bun yields a profit of $0.30.Weenies and Buns would like to know how many hot dogsand how many hot dog buns they should produce each week so asto achieve the highest possible profit.(a) Formulate a linear programming model for this problem.D,I (b) Use the…

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