Total costs K (in billion PLN) and production volume P (in thousand pieces) in the company MIKA are presented in the table: Time, t 1 3 4 K 3 5 8 P 2 4 3 6. 1 Estimate and interpret the parameters of a linear total cost model as a function of as a function of production.
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- The Big Bang Theory Assume the hours needed to cook a meal or done a basket of laundry are different, and they are described below: 1 MEAL 1 BASKET SHELDON 2 1 LEONARD 1/2 2 1. What is the maximum number of meals Sheldon can produce in 12 hours? What is the maximum number of laundry baskets Sheldon can complete in 12 hours? 2. Plot in a graph: Sheldon’s production possibility frontier. 3: Plot in a graph: Leonard’s production possibility frontier. 4. What is Sheldon’s opportunity cost of one meal (in terms of baskets given up)? What is his opportunity cost of one basket (in terms of meals given up)? 5. Does Leonard have an absolute advantage in producing both meals and baskets? 6. Who has a comparative advantage in cooking? 7. Suppose each person has 12 hours for the two tasks in a week, and suppose both Sheldon and Leonard each spend 6 hours on cooking and 6 hours on laundry. Consider an offer from Leonard to Sheldon: do 3 baskets of laundry for me each week, and I’ll cook you 2…A poultry farmer in Lufyanyama has obtained a loan from the Bank to boost his poultry business. He provides you with data to help him optimize the sales. The data is that Old hens can be bought for K20 each but young one cost K50 each. The old hens lay 30 eggs per week, and young ones 50 eggs per week, each egg being worth 30ngwee. A hen cost K10 per week to feed. If a person has only K800 to spend on hens, how many of each kind should he buy to get a profit of more than K600 per week assuming that he cannot house more than 200 hens? a) Formulate the problem as a linear programming model b) Using the Big M – method, how many hens should he buy of each kind to maximize the profit per week? c) Identify the binding and non-binding constraints and justify your choiceFord has four automobile plants. Each is capable of producing the Taurus, Lincoln or Escort but it an only produce one of these cars. The fixed cost of operating each plant for a year and the variable cost of producing a car of each type at the plant are in the table. Variable Cost $ Plant Fixed Cost $ Taurus Lincoln Escort 1 7 billion 12,000 16,000 9,000 2 6 billion 15,000 18,000 11,000 3 4 billion 17,000 19,000 12,000 4 2 billion 19,000 22,000 14,000 Ford faces the following restrictions: each plant can produce only one type of car the total production of each type of car must be at a single plant; that is for examply if any Tauruses are made at plant 1, then all Tauruses must be made there if plants 3 and 4 are used then plant 1 must also be used Each year, Ford must produce 500,000 of each type of car. Question: Formulate an IP whose solution will tell Ford how to minimize the annual cost of producing cars.
- Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets, Bangladesh and Sri Lanka. Demand for Bicycles in these two markets is given by the following Functions: Bangladesh Q1 = 12 – P1 Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) a) Determine the company’s total profit function. Also, (i) What are the profit maximizing levels of price and output for the two markets? (ii) Calculate the marginal revenues in each market. b) Now consider two cases: (i) Company is effectively able to price discriminate in the two markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging the same price in the two markets what are the profit maximizing levels of price, output, and the total profits?…A goldsmith makes two types of jewelry. A model A ring is made with 1 g of gold and 1.5 g of silver and sells for 25 UM.Another model B ring sells for 30 UM and is made of 1.5 g of gold and 1 g of silver. If you only have 750 gof each metal, how many rings should be made of each type to obtain maximum profit?Requested:- Make Initial Table of the problem.- Obtain the Case Variables- Obtain the Objective Function- Get Restrictions- Create the Simplex Table- Obtain the Optimal Solution and the Slack Variables.Solve this operational research exercise.Chiyeyeye Enterprises Ltd sells equestrian boots and has three brands: Riding boots, work boots and casual wear. Looking ahead to the financial year ending 31st may, 2022, the directors of Chiyeyeye Enterprises ltd are faced with a budget loss of ZMW 10 000. Product Riding Boots, work boots Casual Boot Number of units 1000 1000 1000 Sales (ZMW) 12 000 9 000 15 000 Fixed costs 5 000 5 000 7 000 Variable costs 5000 5 000 7 000 Profit 2000 (1000.00) 1000 Calculate the breakeven point for each product? Calculate contribution ratio for each product 3. Can Chiyeyeye close workbooks product line? Explain
- BP Cola must decide how much money to allocate for new soda and traditional soda advertising over the coming year. The advertising budget is $10,000,000. Because BP wants to push its new sodas, at least one-half of the advertising budget is to be devoted to new soda advertising. However, at least $2,000,000 is to be spent on its traditional sodas. BP estimates that each dollar spent on traditional sodas will translate into 100 cans sold, whereas, because of the harder sell needed for new products, each dollar spent on new sodas will translate into 50 cans sold. To attract new customers, BP has lowered its profit margin on new sodas to 2 cents per can as compared to 4 cents per can for traditional sodas. Let X 1 = amount invested in new soda advertising ; and X 2 = amount invested in traditional soda advertising. The objective function that would maximize profit is:nJuicy Juice manufactures different juices made entirely of various exotic nuts. Their primary market is China and they operate 3 plants located in Ethiopia, Tanzania and Nigeria. You have been asked to help them determine where to manufacture the two newest juices they offer, Gingko Nut and Kola Nut. Each plant has a different variable cost structure and capacity for manufacturing the different juices. Also each juice has an expected demand. Cost/unit Gingko Kola Ethiopia ¥21.00 ¥22.50 Tanzania ¥22.50 ¥24.50 Nigeria ¥23.00 ¥25.50 Capacity Units/month Ethiopia 425 Tanzania 400 Nigeria 750 Demand Units/month Gingko 550 Kola 450 same exampe is used but in this case each plant has a different fixed and variable cost structur and cpacity for manufacturing the differnt Juices. the fixed cost only applies if the plant produces any juice Capacity Unit-Month Fixed…nJuicy Juice manufactures different juices made entirely of various exotic nuts. Their primary market is China and they operate 3 plants located in Ethiopia, Tanzania and Nigeria. You have been asked to help them determine where to manufacture the two newest juices they offer, Gingko Nut and Kola Nut. Each plant has a different variable cost structure and capacity for manufacturing the different juices. Also each juice has an expected demand. Cost/unit Gingko Kola Ethiopia ¥21.00 ¥22.50 Tanzania ¥22.50 ¥24.50 Nigeria ¥23.00 ¥25.50 Capacity Units/month Ethiopia 425 Tanzania 400 Nigeria 750 Demand Units/month Gingko 550 Kola 450 How much of each juice should be made at each plant in order to minimize total cost while meeting demand and adhering to plant capacity?
- A bed mart company is in the business of manufacturing beds andpillows. The company has 40 hours for assembly and 32 hours forfinishing work per day. Manufacturing of a bed requires 4 hours forassembly and 2 hours for finishing. Similarly a pillow requires 2 hoursfor assembly and 4 hours for finishing. Profitability analysis indicatesthat every bed would contribute Birr 80, while a pillow contribution isBirr 55 respectively. Find out the daily production of the company tomaximise the contribution (profit). Solve the problem by graphicalmethodConsider a monopolistically competitive market with NN firms. Each firm's business opportunities are described by the following equations: Demand: Q=100N−PQ=100N−P Marginal Revenue: MR=100N−2QMR=100N−2Q Total Cost: TC=50+Q2TC=50+Q2 Marginal Cost: MC=2QMC=2Q How much profit does each firm make? a: 1,250/N*2−50 b: 2,500/N*2−50 c: 50+625/N*2 d: 1,875/N*2 In the long run, how many firms will exist in this market?Given this linear programming model, solve the model and then answer the questions that follow.Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc.Subject toMachine 5x1 + 4x2 + 3x3 ≤ 160 minutes Labor 4x1 + 10x2 + 4x3 ≤ 288 hoursMaterials 2x1 + 2x2 + 4x3 ≤ 200 poundsProduct 2 x2 ≤ 16 units x1, x2, x3 ≥ 0 a. Are any constraints binding? If so, which one(s)?