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- Bag Company produces leather jackets and handbags. A jacket requires of leather and a handbag only . The labor requirements for the two products are 12 and 5 hours respectively. The current weekly supplies of leather and labor are limited to and 1,850 hours. The company sells the jackets for $350 and the handbags for $120. The objective is to determine the production schedule that maximizes the net revenue. In this document, write the mathematical formulation of both the primal and the dual problems. In the Excel file used in problem 1, solve the primal problem and generate a Solver sensitivity report in a new worksheet. In this document, use the Solver sensitivity report to answer the following two questions: What is the maximum purchase price the company should pay for additional leather? What is the maximum amount the company should pay for additional labor?Auria will produce 3 vehicle components and knows that each start generates a cost of 5,000 pesos. The cost of the units is $ 200, $ 100 and $ 70 respectively. Annual demand is 100,000 units for Product A, 150,000 units for Product B, and 200,000 units for Product C. The inventory rate is 15% per month. Product A and B are basic and substitutable products, so there must be a minimum average inventory of 8,000 units of both. The company seeks a maximum of $ 100,000 invested money in inventory. The available warehouse space is 400m3 and product A occupies 0.5m3, product B 0.7m3 and C 1m3. Consider that product A and C allow shortages and the goodwill loss cost is $ 3 for each unit of those items. a) Formulate the problem as a mathematical programming model (objective function and constraints) that minimizes the total annual costA manufacturing process has 12 workers and 6 stations. The process iscompleted in the order given below. Where there are multiple workers within a station,each worker works independently on his/her own unit. Assume inventory buffers areallowed between each station.Station Staffing Processing time (hoursper unit per worker)A 2 2.20B 1 1.25C 3 2.00D 2 2.60E 3 3.00F 1 0.75What is the maximum number of units per hour that can be produced? Assume they startthe day with inventory at each station to work on
- The poultry farmer decided to make his own chicken scratch by combining alfalfa and corn in rail car quantities. A rail car of corn costs $400 and a rail car of alfalfa costs $200. The farmer's chickens have a minimum daily requirement of vitamin K (500 milligrams) and iron (400 milligrams), but it doesn't matter whether those elements come from corn, alfalfa, or some other grain. A unit of corn contains 150 milligrams of vitamin K and 75 milligrams of iron. A unit of alfalfa contains 250 milligrams of vitamin K and 50 milligrams of iron. Formulate the linear programming model for this situation. Group of answer choices Min Z = $450C + $200A Subject to: 150C + 250A ≥ 500 75C + 50A ≥ 400 C, A ≥ 0 Min Z = $400C + $200A Subject to: 150C + 250A ≥ 500 75C + 50A ≥ 400 C, A ≥ 0 Max Z = $400C + $500A Subject to: 150C + 250A ≥ 500 75C + 50A ≥ 400 C, A ≥ 0 Max Z = $400C + $200A Subject to: 150C + 250A ≥ 500 75C + 50A ≥ 400 C, A ≥ 0 Min Z = $400C + $200A Subject to: 150C + 250A ≥ 400…ProHaul specializes in trans-American shipments for businesses through the delivery of containers. For every container the company loads on its trucks, ProHaul estimates the haul costs $1,000. In addition, containers are weighed and for each pound, there are hauling fees of $0.15. ProHaul plans to charge $0.49 per pound to his customers.How many pounds would a container have to hold in order for the company to Break Even?The aggregate demand for a product line for the next 6 months is given below. The firm has regular capacity of 120 units per month, overtime capacity for 40 more units per month, and subcontracting can supply up to 100 units per month. Month 1 2 3 4 5 6Demand 220 160 200 210 200 190Additional DataPrevious output level 150 unitsBeginning inventory 100 unitsShortage cost K250 per unit per monthInventory holding cost K100 per unit per monthRegular time cost K1200 per unitSubcontracting cost K2000 per unitOvertime cost K1500 per unitHiring workers to increase production level K200 per unitFiring workers to decrease production level K500 per unitUse the Chase Strategy and answer the following questions Using the data given If the regular capacity is increased to 210 from the current level of 120 units per month and you meet your demand by only regular time production, then answer the…
- The aggregate demand for a product line for the next 6 months is given below. The firm has regular capacity of 120 units per month, overtime capacity for 40 more units per month, and subcontracting can supply up to 100 units per month. Month 1 2 3 4 5 6Demand 220 160 200 210 200 190Additional DataPrevious output level 150 unitsBeginning inventory 100 unitsShortage cost K250 per unit per monthInventory holding cost K100 per unit per monthRegular time cost K1200 per unitSubcontracting cost K2000 per unitOvertime cost K1500 per unitHiring workers to increase production level K200 per unitFiring workers to decrease production level K500 per unitUse the Chase Strategy and answer the following questions. a. What is the total cost of shortagesand the cost of overtime production? b. What is the cost of subcontracting? c. What is the cost of increasing production level?Greener Pastures Incorporated (GPI) produces a highquality organic lawn food and weed eliminator called SuperGreen (SG). Super Green is sold in 50-pound bags. Monthlydemand for Super Green is 75,000 pounds. Greener Pastures hascapacity to produce 24,000 50-pound bags per year. Th e setup costto produce Super Green is $300. Annual holding cost is estimatedto be $3 per 50-pound bag. Currently, GP is producing in batchesof 2500 bags.(a) Calculate the total annual costs of the current operatingpolicy at GPI.(b) Calculate the economic production quantity (EPQ).(c) Calculate the total annual costs of using the EPQ.(d) Calculate the penalty cost incurred with the presentpolicy.Information on a business is given below.Variable Expenses:Raw material expense: 250 TL / pieceAuxiliary equipment expense: 150 TL / pieceElectricity expenses: 100 TL / pieceSpare parts expense: 75 TL / pieceOther variable expenses: 125 TL / pieceFixed costs:Depreciation, interest and insurance expenses: 75 000 TLLabor and personnel expenses: 250 000 TLOther fixed expenses: 115 000 TLProduction capacity: 2000 pcs / monthSale price: 1600 TL / pieceAccording to the above,a) Find the break-even point as the production quantity?b) Find the amount that the business has to produce in order to make a profit of 500 000 TL / month?
- (Need both parts a and b) During the next four months, a customer requires, respectively, 500, 650, 1000, and 700 units of a commodity, and no backlogging is allowed (that is, the customer’s requirements must be met on time). Production costs are $50, $80, $40, and $70 per unit during these months. The storage cost from one month to the next is $20 per unit (assessed on ending inventory). It is estimated that each unit on hand at the end of month 4 can be sold for $60. Assume there is no beginning inventory. A. What is the objective function in this problem? B. What are the constraints in this problem? Write algebraic expressions for eachNature's Garden Inc. produces wood chips, wood pulp, and mulch. These products are produced through harvesting trees and sending the logs through a wood chipper machine. One batch of logs produces 20,304 cubic yards of wood chips, 14,100 cubic yards of mulch, and 9,024 cubic yards of wood pulp. The joint production process costs a total of $32,000 per batch. After the split-off point, wood chips are immediately sold for $25 per cubic yard while wood pulp and mulch are processed further. The market value of the wood pulp and mulch at the split-off point is estimated to be $22 and $24 per cubic yard, respectively. The additional production process of the wood pulp costs $5 per cubic yard, after which it is sold for $30 per cubic yard. The additional production process of the mulch costs $4 per cubic yard, after which it is sold for $32 per cubic yard.Hot Breads, a popular baker in Dhaka makes two types of cakes. To make one dozen ofpremium pound cake requires 3 kilos of flour, 1 kilo sugar, and 1 kilo butter. Making one dozenof our best requires 6 kilos of flour, 0.5 kilo of sugar, and 1 kilo of butter. Hot bread has in itsstock 150 kilograms of flour, 22 kilograms of sugar, and 27.5 kilograms of butter. The premiumcakes sell for 20 taka per dozen and our best sells for 30 taka per dozen. How many dozens ofeach cake Hot Breads should make to maximize revenue?a. Write the information given in the question in a tabular format.b. Write the problem in a linear programming format.c. Indentify the feasible zone.d. Find the revenue maximizing levels of production for scrapers and brushes.e. Is there any excess capacity in any machine?f. Find the amount of excess capacity.