Ruffa's diet requires that all the food she eat come from the four basic food groups: chocolate cake, ice cream, soda and french fries. At present four foods are available: brownies, chocolate ice cream, cola and cheese flavored french fries. The cost of the foods (in cents) and my daily nutritional requirements together with their calorie, chocolate, sugar and fat contents are listed in the table below. Find the optimal solution of this diet problem. Brownie Chocolate ice cream Cola cheese flavored french fries Requirement Calories Chocolate Sugar Fat Price 400 2 2 50 200 2 4 20 150 4 1 30 500 0 7 80 500 10 8 32006
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- Emily works for a small software company and oversees software quality assurance. The company recently developed an inventory control system for a national clothing manufacturer. The system gathers sales information on an hourly basis from clothing retailers nationwide. This information is then used by all departments (including the accounting, shipping, and ordering departments) to control the functions of the clothing manufacturer. Emily suspects that the inventory functions of the system are not sufficiently tested, although they have passed all their contracted (legal) tests. However, she is pressured by her employers to sign off on the software. Whilst she is only required to perform tests which have been agreed to in the original contract, her considerable experience in software testing has led her to be concerned over the quality of the system. Her employers say that they will go out of business if they do not deliver the software on time. Emily knows that if any section of…A dietitian has been asked by the athletic director to develop a snack that athletes can use in their training programs. The dietitian intends to mix two seperate products to make the snack. The following information (on the table below): Product A costs Php20 per ounce, while Product B costs Php10 per ounce. Determine the optimal quantities of each product that will give the minimized cost.Hot Oven daily requirements of 70 g of protein, 1 g calcium, 12 mg iron, and 3000 calories are needed for a balanced diet. The following foods are available for consumption with the cost and nutrients per 100 g as shown. protien (g) calories calcium(g) iron(mg) cost (ghc) brown bread 12.0 246 0.1 3.2 0.5 cheese 24.9 432 0.2 0.3 20 butter 0.1 793 0.03 0.0 1.0 baked beans 6.0 93 0.05 2.3 0.25 spinach 3.0 26 0.1 2.0 0.25 The objective of the Hot Oven is to find a balanced diet with minimum cost.a) Formulate a linear programming model for this problem. b) Use solver to find optimal solution and sensitivity report. c) Management have asked you to determine the optimal solution. Write your answer in a form of a report to be submitted to the management. d) Advice the management about objective function value corresponding to your answer in (b)
- Trips Logistics, a third-party logistics firm that provides warehousing and other logistics services, is facing a decision regarding the amount of space to lease for the upcoming three-year period. The general manager has forecast that Trips Logistics will need to handle a demand of 100,000 units for each of the next three years. Historically, Trips Logistics has required 1,000 square feet of warehouse space for every 1,000 units of demand. For the purposes of this discussion, the only cost Trips Logistics faces is the cost for the warehouse. Trips Logistics receives revenue of $1.22 for each unit of demand. The general manager must decide whether to sign a three-year lease or obtain warehousing space on the spot market each year. The three-year lease will cost $1 per square foot per year, and the spot market rate is expected to be $1.20 per square foot per year for each of the three years. Trips Logistics has a discount rate of k = 0.1.The Rotary Club is holding a pizza sale to finance outreach projects. The Club made an agreement to purchase pizza from Pizza Hut at a 30% discount which the Rotary Club can thên resell for a profit. It is expected that of the 500 families in the community, at most 70% will buy Pizza. Based on a survey of their personal preferences, the students believe that they should order no more than 120 cheese pizzas, no more than 150 pepperoni pizzas, and no more than 100 vegetarian pizzas. They also want to make sure that at least 20% of the total pizzas are cheese and at least 50% of the pizzas are pepperoni. The standard price (before discount) for the cheese, pepperoni and vegetarian is $12, $15 and $14, respectively. The Rotary Club makes a profit of 10%, 15% and 20%, respectively, for each cheese, pepperoni, and vegetarian pizza they resell Formulate a linear programming model that would determine the optimal solution.Jasmine is a mother of three children, ages 6 months, 2 years, and 3 and a half. Jasmine makes $24,000 a year at her full-time job, while her husband, Jamal, makes $45,000 a year. The daycare their children attend currently costs them $18,000 a year for all three children, but next year the cost is going up to $21,000. Jasmine wonders whether it’s even worth working, when she spends so much of her salary on childcare, and is considering quitting her job completely or working part-time instead. Jasmine’s dilemma is an example of a gendered process that occurs in the point of overlap of which two institutional arenas? the market and the family the family and the state the family and religion the state and the market
- The Fish House (TFH) in Norfolk, Virginia, sells fresh fish and seafood. TFH receives daily shipments of farm-raised trout from a nearby supplier. Each trout costs $2.45 and is sold for $3.95. To maintain its reputation for freshness, at the end of the day TFH sells any leftover trout to a local pet food manufacturer for $1.25 each. The owner of TFH wants to determine how many trout to order each day. Historically, the daily demand for trout is: Demand 10 11 12 13 14 15 16 17 18 19 20 Probability 0.02 0.06 0.09 0.11 0.13 0.15 0.18 0.11 0.07 0.05 0.03 a. Construct a payoff matrix for this problem. b. How much should the owner of TFH be willing to pay to obtain a demand forecast that is 100% accurate? give a clear explanation for (b)GreenLawns 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…Use the table below to answer the following question(s). Fiberia Accessories, a clothing retailer, is planning to introduce a new line of sweaters as part of the winter collection for $65 with an inventory of 1500. The main selling season is 60 days between November and December. The store then sells the remaining units in a clearance sale at 65 percent discount. Out of the 60 main retail days, Fiberia sells the sweaters at full retail price for only 45 days, while giving a discount of 25 percent for the remaining 15 days. The demand functions a, and b are given as 79.5 and 1.1 respectively. Marked Down Pricing Model for Fiberia Accessories's new sweater Data Retail Price Inventory Selling Season (days) Days at Full Retail Intermediate Markdown Clearance Markdown Demand Function A B $65 1500 60 45 25 percent |65 percent 79.5 1.1 Compute the everyday sales throughout the discount sales period.
- The Sunrise Raisin Company makes three different products from raisins: natural raisins (Natural), lightly coated yogurt raisins (Light), and heavily coated yogurt raisins (Heavy). The company is barely able to keep up with the increasing demand for these products. However, increasing raw material prices and market competition are forcing the company to watch its margins to ensure it is operating in the most efficient manner possible. To meet marketing demands for the coming week, the company needs to produce no more than 500 pounds of the Natural product, between 50 and 600 pounds of the Light product, and no more than 400 pounds of the Heavy product. Each pound of the Natural, Light, and Heavy product contains, respectively, 100%, 80%, and 50% raisins with the remaining weight made up of yogurt coating. The company has 825 pounds of raisins and 420 pounds of yogurt available for use in the next week. The various products are made by using three different machines that coat the…Read the following passage and answer the question that follows Quincy Snodgrass Enterprises—Forecasting Quincy Snodgrass is an entrepreneur and a lover of the outdoors. He has worked for various companies since he graduated college with his business administration degree in management. Over the years, he has saved every extra penny and now has the starting capital he needs; consequently, he plans to open his own business. Quincy plans to open a landscaping business. The primary services he’ll offer are grass cutting, edging, and bush trimming. Obviously, this will only provide income in the spring, summer, and early fall. Therefore, he plans to offer snow removal in the winter. His goal is to continue to provide those baseline services and expand into actual landscaping work. Quincy’s initial challenge is to develop a forecast of how many customers he’ll have each month. This is essential to determine if he needs to hire any additional labor throughout the season. Unfortunately, none…Read the following passage and answer the question that follows Quincy Snodgrass Enterprises—Forecasting Quincy Snodgrass is an entrepreneur and a lover of the outdoors. He has worked for various companies since he graduated college with his business administration degree in management. Over the years, he has saved every extra penny and now has the starting capital he needs; consequently, he plans to open his own business. Quincy plans to open a landscaping business. The primary services he’ll offer are grass cutting, edging, and bush trimming. Obviously, this will only provide income in the spring, summer, and early fall. Therefore, he plans to offer snow removal in the winter. His goal is to continue to provide those baseline services and expand into actual landscaping work. Quincy’s initial challenge is to develop a forecast of how many customers he’ll have each month. This is essential to determine if he needs to hire any additional labor throughout the season. Unfortunately, none…