Concept explainers
a)
To determine: The daily dessert plan that stays with her constraints and minimizes the total taste index using solver.
Introduction: In linear programming, the unbounded solution would occur when the objective function is infinite. If no solution satisfied the constraints, then it is said to be an unfeasible solution.
b)
To draw: The daily desserts plan which would minimize the total taste index and stays within her constraints.
Introduction: In linear programming, the unbounded solution would occur when the objective function is infinite. If no solution satisfied the constraints, then it is said to be an unfeasible solution.
c)
To determine: The way optimal plan varies when the calorie varies.
Introduction: In linear programming, the unbounded solution would occur when the objective function is infinite. If no solution satisfied the constraints, then it is said to be an unfeasible solution.
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Chapter 3 Solutions
Practical Management Science
- The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.arrow_forwardSapphire Farm is a business that trains and boards horses and educates young riders about horse care, nutrition, and riding. The farm provides both a learning and a fun environment for young equestrians and their families. It also hosts horse shows for beginning riders to help them build confidence in the show ring and to prepare them for local horse shows by running shows in accordance with the rules and regulations of the National Hunter Jumper Association. Feedback from the horseshow judges are provided to all riders so they can do better at their next meet. In addition, all warm-up and training areas are fenced and monitored by adults for the children's safety. If the farm unintentionally hired someone to teach riding who was unable to deal effectively with small children, then a _____ would occur. A. service divergence B. quality underperformance C. performance breakdown D. product variation E. customer aberrationarrow_forwardDigital Controis, Inc. (DCI), manufactures two models of a radar gun used by police to monitor the speed of automobiles. Model A has an accuracy of plus or minus 1 mile per hour, whereas the smaller model B has an accuracy of plus or minus 3 miles per hour. For the next week, the company has orders for 100 units of model A and 150 units of model B. Although DCI purchases all the electronic components used in both models, the plastic cases for both models are manufactured at a DCI plant in Newark, New Jersey. Each model A case requires 4 minutes of injection-molding time and 6 minutes of assembly time. Each model B case requires 3 minutes of injection-molding time and 8 minutes of assembly time. For next week, the Newark plant has 600 minutes of injection-molding time avallable and 1,080 minutes of assembly time availab The manufacturing cost is $10 per case for model A and $6 per case for model B. Depending upon demand and the time avalable at the Newark plant, DCI occasionally…arrow_forward
- Salt & Pepper & Co (Salt & Pepper) is a firm of Chartered Certified Accountants which has seen its revenue decline steadily over the past few years. The firm is looking to increase its revenue and client base and so has developed a new advertising strategywhere it has guaranteed that its audits will minimise disruption to companies as they will not last longer than two weeks. In addition, Salt & Pepper has offered all new audit clients a free accounts preparation service for the first year of the engagement, as it is believed that time spent on the audit will be reduced if the firm has produced the financial statements. The firm is seeking to reduce audit costs and has therefore decided not to update the engagement letters of existing clients, on the basis that these letters do not tend to change much on a yearly basis. One of Salt & Pepper’s existing clients has proposed that this year’s audit fee should be based on a percentage of their final pre-tax profit. The…arrow_forwardMonica Britt has enjoyed sailing small boats since she was 7 years old, when her mother started sailing with her. Today, Monica is considering the possibility of starting a company to produce small sailboats for the recreational market. Unlike other mass-produced sailboats, however, these boats will be made specifically for children between the ages of 10 and 15. The boats will be of the highest quality and extremely stable, and the sail size will be reduced to prevent problems of capsizing. Her basic decision is whether to build a large manufacturing facility, a small manufacturing facility, or no facility at all. With a favourable market, Monica can expect to make R90,000 from the large facility or R60,000 from the smaller facility. If the market is unfavourable, however, Monica estimates that she would lose R30,000 with a large facility and she would lose only R20,000 with the small facility. Because of the expense involved in developing the initial moulds and acquiring the…arrow_forwardMonica Britt has enjoyed sailing small boats since she was 7 years old, when her mother started sailing with her. Today, Monica is considering the possibility of starting a company to produce small sailboats for the recreational market. Unlike other mass-produced sailboats, however, these boats will be made specifically for children between the ages of 10 and 15. The boats will be of the highest quality and extremely stable, and the sail size will be reduced to prevent problems of capsizing. Her basic decision is whether to build a large manufacturing facility, a small manufacturing facility, or no facility at all. With a favourable market, Monica can expect to make R90,000 from the large facility or R60,000 from the smaller facility. If the market is unfavourable, however, Monica estimates that she would lose R30,000 with a large facility and she would lose only R20,000 with the small facility. Because of the expense involved in developing the initial moulds and acquiring the…arrow_forward
- Lynette is interested in finding a sedan car for work. Below is the summary of her criteria and the choices that she has selected as potential cars that she may purchase. She wants you to find out the best alternative based on these data. Note: Calculate the data given below in the same way as the rating scale. There is no need to convert the data into the rating scale before the calculation. Criteria Weight Toyota Camry Volkswagen Passat Mazda 6 Hyundai Sonata Objective Drive-away price 8 $51,673 $57,399 $55,040 $55,692 Min Engine size (L) 3 2.5 2.0 2.5 2.5 Max Fuel tank capacity (L) 5 50 66 62 60 Max Power:Weight (W/kg) 5 97.3 108.3 104.8 130.2 Max Max torque (Nm) 4 221 350 420 422 Max Fuel consumption (L/100km) 7 4.7 6.9 7.6 8.1 Min Service cost (5 yr) 6 $1,940 $2,692 $2,310 $1,446 Minarrow_forwardGreenLawns provides a lawn fertilizing and weed control service. The company is adding a special aeration treatment as a low-cost extra service option, which it hopes will help attract new customers. Management is planning to promote this new service in two media: radio and direct-mail advertising. A media budget of $4 (in thousands)is available for this promotional campaign. Based on- past experience in promoting its other services, GreenLawns has obtained the following estimate of the relationship between sales and the amount spent on promotion in these two media: S-2R2-12M2-9RM + 20R +37M, Where S = total sales R = amount spent on radio advertising M = amount spent on direct-mail advertising GreenLawns would like to develop a promotional strategy that will lead to maximum sales subject to the restriction provided by the media budget. The problem is formulated as below: Max -2R2-12M²-9RM+20R+37M s.t. 1R+1M=0 Using Excel Solver, solve the above nonlinear optimization model. (a) What…arrow_forwardTattle Tots makes a fiberglass tricycle for kids that is composed of three major components: a handlebar-front wheel-pedal assembly, a seat, and frame unit, and rear wheels. The company has orders for 12,000 of these tricycles. The company does not have the resources available to manufacture everything needed for the completion of 12,000 tricycles so it has gathered purchase information for each component. The following table shows relevant information: Requirements Cost to Manufacture Cost to Purchase Component Plastic Time Space Front 3 10 2 8 12 Seat/Frame 4 6 2 6 9 Rear-wheel (each) .5 2 .1 1 3 Available 50,000 160,000 30,000 Develop a linear programming model to advise the operations manager of Tattle Tots how many of each component should be manufactured and how many should be purchased in order to provide 12,000 fully completed tricycles at the minimum cost. What is your best…arrow_forward
- (a) Determine the amount of potatoes and green beans Maria should purchase each week for the casserole to minimize the ingredient costs while meeting nutritional, taste, and demand requirements. Before she makes her final decision, Maria plans to explore the following questions independently except where otherwise indicated. (b) Maria is not very concerned about the taste of the casserole; she is only concerned about meeting nutritional requirements and cutting costs. She therefore forces Edson to change the recipe to allow for only at least a one to two ratio in the weight of potatoes to green beans. Given the new recipe, determine the amount of potatoes and green beans Maria should purchase each week. (c) Maria decides to lower the iron requirement to 65 mg since she determines that the other ingredients, such as the onions and cream of mushroom soup, also provide iron. Determine the amount of potatoes and green beans Maria should purchase each week given this new iron…arrow_forwardA company is operating in two unrelated businesses. The first one is making common salt, which is sold in one kilogram consumer packs. The second business is making readymade garments. The owner of the businesses has decided to implement Materials Requirement Planning (MRP) in one of the two businesses, which is likely to give him greater benefit. Assuming that the current turnover and profits of both the units are comparable, compare the relative benefits and limitations of Materials Requirement Planning (MRP) for these two businesses.arrow_forwardThe Marketing Manager of Dotcom Limited has conducted a market research on the price-demand relationship for its consumer durable Product-V which has been recently launched. The price-demand pattern will be as follows: Price per unit (Rs.) 16.650 16.050 14.400 13.050 Product-V is manufactured in batches of 1.000 units. The production manager of Dotcom Limited has also researched and studies the pattern and believes that 50% of the variable manufacturing cost would have a learning effect. This learning curve effect will continue up to 4.000 units of production at constant rate But after 4.000 units of production unit variable manufacturing cost would be equal to the unit cost at the 4 batch. The manufacturing unit cost of the first batch will be Rs. 6.600 of which only 50% is subjected to learning and experience curve effect. The average unit variable of all 4 batches will be Rs 6.180 The price and maximum contribution at which Dotcom Limited should sell Product-V is: Rs.14,400, Rs.…arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,