Jimmy's Appliance Company manufactures washers and dryers. Each washer re 2 hours of assembly time and 50 pounds of steel. Each dryer requires 3 hours of assembly time and 30 pounds of steel. Each washer generates $90 of profit and eac ryer generates $65 of profit. There are only 150 hours of assembly time and 1,95C ounds of steel available per week. Lastly, the company has limited motor components and can produce at most 20 dryers each week. Formulate as a linear rogramming problem, and determine the value of the objective function at the Otimal solution.
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- 2.28 A foundry produces castings to order. An order for 20 special castings has been re- ceived. Since the casting process is highly variable, not all castings produced are good. The cost of producing each casting is $550; the additional cost of finishing a good casting is $125. If a casting is not good, it is recycled at a value of $75; excess good castings are not finished but are recycled at a value of $75. The customer has agreed to accept 15, 16, 17, 18, 19, or 20 castings at a price of $1250 each. If fewer than 15 good castings are produced, none will be purchased by the customer. Prob- ability distributions for the number of good castings produced in a batch of varying sizes are given below. How many castings should be scheduled in order to maximize expected profit? #Good Castings 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 79 2 PRODUCT, PROCESS, AND SCHEDULE DESIGN Number of Castings Scheduled 15 16 17 0.05 0.00 0.00 0.00 0.00 0.00 0.05 0.05 0.00…The Delta company uses three raw materials to make cakes. Delta is trying to reduce warehousing costs and establishes three policies to that end: i) The annual number of orders for all products must be at least 20 per contractual terms with transportation providers. ii) The average inventory in units must be a maximum of 1800. iii) Because the raw material is perishable, there can never be more than 2000 units in inventory of raw material 1. Raw material 2 has a maximum allowed of 1200 units and the raw material 3 can store maximum 400 units. The following table shows the product information: Materia Demanda Costos por unidad Costo por prima (u/año) ordenar ($) 2200 2 300 2 500 4 650 3 3000 10 100 Consider an interest rate of 10% per year. A) Formulate the problem as a mathematical programming model that minimizes the total annual cost. b) Represent the problem in a single equation including the constraints in terms of lambda c) Find the optimized batch sizes for the company's raw…List the system of inequalities which describe B in the graph below.ECON1003 Mathematics for Social Sciences Unit 3_Version 1 Page 33 6. Anya’s Jeans has production process organized in threedistinct stages: cutting; sewing and finishing. She produces threetypes of jeans, namely peddle-pushers, hipsters and low cuts. Thenumber of minutes each type requires in each production processin shown below.Type Cutting Sewing FinishingPeddle-Pusher 4 6 2Hipster 6 7 4Low Rider 9 3 6On average, there are 6400 minutes of cutting time, 3500 minutes ofsewing time and 2400 minutes of finishing time each day. Given thatthe company makes $10 profit on each peddle-pusher $ 50 on eachhipster and $60 on each low cut and that the company sells all thejeans made. List the system of inequalities for the cutting, sewingand finishing constraints.
- Sarah's Organic Soap Company makes four kinds of organic liquid soap: regular, lavender, citrus, and tea tree. The demand for the four scents are 150, 120, 75, and 50 kg per hour respectively. Sarah's production process can produce any soap at the rate of 450 kg per hour, but 1.5 hours are needed to switch between scents. During those switchover times, the process doesn't produce any soap. Sarah wants to choose a production schedule that (i) cycles repeatedly through the four scents, (ii) meets the required demand and (iii) minimizes the amount of inventory held. Sarah needs to purchase organic palm oil to make her soaps. She needs 1,000 kg of palm oil per day on average. The supplier charges a $60 delivery fee per order (which is independent of the order size) and $4.75 per kg. Sarah's annual holding cost is 25%. Assume 52 weeks per year and 5 days per week. If Sarah wants to minimize inventory holding and ordering costs, how much palm oil should she purchase with each order (in kg)?…The Frist Corporation has the followinginternal controls related to inventory:1. Only authorized inventory warehousing personnel are allowed in inventory storageareas.2. All inventory products are stored in warehousing areas that are segregated fromother storage areas used to house equipment and supplies.3. All inventory held on consignment at Frist Corporation is stored in a separatearea of the warehouse.4. The inventory purchasing system only allows purchases from pre-approved vendors.5. The perpetual inventory system tracks the average number of days each inventoryproduct number has been in the warehouse.6. Microchips are embedded in each product and when inventory items are removedfrom the warehouse to shipping, radio-frequencies signal a deduction of inventoryto the perpetual inventory system.7. On a weekly basis, inventory accounting personnel take samples of inventoryproducts selected from the perpetual inventory system and verify that the inventoryis on-hand in the warehouse…Mazoon Company sells 500 units resulting in $150,000 of sales revenue, $50,000 of variable costs, and $36,000 of :fixed costs. The number of units that must be sold to achieve $40,000 of operating income is units 380 a O None of the given answers b O units 200 .c O units 152 d O units 390 .e O
- Princetown paints ltd manufactures three basic types of paint. emulsion, gloss, and undercoat. using the same mixing machines and direct labour for each of the three products. the Management accountant of Princetown paints was faced with the task of arranging the weekly production for his company. information about the sale price and costs per 100 liters is given in the following table ( all figures in $). sales price per 100 liters ( emulsion 120), ( gloss 126), ( undercoat 110). variable cost per 100 liters ( emulsion 120), ( gloss 126), ( undercoat 110). direct material costs ( emulsion 11), ( gloss 25), ( undercoat 20). direct labour costs ( emulsion 30), ( gloss 36), ( undercoat 24). mixing costs ( emulsion 32), ( gloss 20), ( undercoat 36). other variable costs ( emulsion 12), ( gloss 15), ( undercoat 10). the cost of direct labour is $3 per hour and the variable cost of mixing is $4 per hour. in any one week, direct labour hours are restricted to 8000 hours and mixing machine…Glams Touch is a budding cosmetics family business in Sekondi. The owners, Baaba Benson and Bernard Benson, must ensure that they judiciously use the store space available. They have never kept detailed inventory or sales records. They immediately place new items on the shelves as soon as shipment of goods arrives.Invoices from suppliers are only kept for tax purposes. During sales, they record the items numbers and the total amount received at the cash register. The owners use their own judgment in identifying items that need to be reordered. Baaba and Bernard rely on their own judgment in deciding the cosmetics that need to be restocked.Analyse the business implication of this situation. In your view, how could information systems be utilized to assist the Bensons manage Glams Touch. Enumerate some data that should be captured by the systems and what information outputs are to be churned out from the system.Mack’s guitar fabrication shop produces low cost, highly durable guitars for beginners. Typically, out of the 100 guitars that begin production each month, only 80 percent are considered good enough to sell. The other 20 percent are scrapped due to quality problems that are identified after they have completed the production process. Each guitar sells for $300. Because some of the production process is automated, each guitar only requires 10 labor hours. Labor is paid at $10/hour, materials cost is $40/guitar, and overhead is $2,000. a) Calculate the labor and multifactor productivities. b) After some study, the operations manager recommends 3 options to improve the company’s multifactor productivity: (1) increase the sales price by 10 percent, (2) improve quality so that only 10 percent are defective, or (3) reduce labor, material, and overhead costs by 10 percent. Which option has the greatest impact on the multifactor productivity measure?
- Tom is a habitual shopper at garage sales. Last Saturday he stopped at one where there were several types of used building materials for sale. At the low prices being asked, Tom knew that he could resell the items in another town for a substantial gain. Four things stood in his way: he could only make one round trip to resell the goods; his pickup truck bed would hold only 1200 pounds; the pickup truck bed could hold at most 80 cubic feet of merchandise; and he had only $190 cash with him. He wants to load his truck with the mix of materials that will yield the greatest profit when he resells them. Formulate (define objective function and constraints) and solve this problem (using excel solver) as a linear program.. A commercial orchard grows, picks, and packs apples and pears. A peck (quarter bushel) of apples takes 4 minutes to pick and 5 minutes to pack; a peck of pears takes 5 minutes to pick and 4 minutes to pack. Only one picker and one packer are available. How many pecks each of apples and pears should be picked and packet every hour (60 minutes) if the profit is $3/peck for apples and $2/peck for pears? Solve graphically as a linear program and confirm analytically.A brewery produces regular beer and a lower-carbohydrate "light" beer. Steady customers of the brewery buy 12 units of regular beer and 18 units of light beer monthly. While setting up the brewery to produce the beers, the management decides to produce extra beer, beyond that needed to satisfy customers. The cost per unit of regular beer is $32,000 and the cost per unit of light beer is $60,000. Every unit of reqular beer brings in $100,000 in revenue, while every unit of light beer brings in $300,000 in revenue. The brewery needs at least $9,000,000 in revenue, and has determined that the total demand will be at least 50 units of beer. Complete parts (a) and (b). (a) How much of each type of beer should be made so as to minimize total production costs? 30 units of regular beer and 20 units of light beer should be made, for a minimum total cost of $ 2160000 (Type integers or decimals.) (b) Suppose the minimum revenue is increased to $9,400,000. Use shadow costs to calculate the total…