Set up the objective function and enumerate all the constraints, Define the decision variables of the IP Programming problem
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- Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?what is the shawdow price of constraint 1?
- A paper-recycling plant processes box board, tissuepaper, newsprint, and book paper into pulp that can be usedto produce three grades of recycled paper (grades 1, 2, and3). The prices per ton and the pulp contents of the fourinputs are shown in Table 82. Two methods, de-inking andasphalt dispersion, can be used to process the four inputsinto pulp. It costs $20 to de-ink a ton of any input. Theprocess of de-inking removes 10% of the input’s pulp,leaving 90% of the original pulp. It costs $15 to applyasphalt dispersion to a ton of material. The asphalt dispersionprocess removes 20% of the input’s pulp. At most, 3,000tons of input can be run through the asphalt dispersionprocess or the de-inking process. Grade 1 paper can only beproduced with newsprint or book paper pulp; grade 2 paper,only with book paper, tissue paper, or box board pulp; andgrade 3 paper, only with newsprint, tissue paper, or boxboard pulp. To meet its current demands, the company needs500 tons of pulp for grade 1…Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pen...Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pens are given below.Fliptop Model Tiptop Model AvailablePlastic 3 4 36Ink Assembly 5 4 40Molding Time 5 2 30The profit for either model is $1000 per lot.What is the linear programming model for this problem?What are the boundary points of the feasible region?What is the profitability at each boundary point of the feasible region?Find the optimal solution.1. A distillery produces two types of alcohol for filling and distributing, the regular beer and the premium beer. A batch of regular costs $375 to manufacture and a container of the Premium beer costs $420. The manufacturer wishes to establish the weekly production plan that minimizes cost. Production of these products is limited to processing, testing and material. Each batch of regular beer requires 4 hours processing whereas each batch of premium requires 2 hours of processing. Further each batch of regular requires 4 hours of testing compared to 6 hours of testing for a batch of Super. A batch of regular and a batch of Super each require 1 litre of material. Processing and testing have a maximum of 100 and 180 hours available and the total material available is 40 litres. Because of an agreement, the sales of regular beer are limited to a weekly maximum of 20 batches and to honour an agreement with a loyal distributor, at least 10 batches of premium beer must be sold each week.…
- 2. A firm makes two products X and Y and has a total production capacity of 9 tons per day.X and Y requiring the same production capacity. The same has a permanent contract to supply at least two tons of X and at least 3 tons of Y per day to another company. Each ton of X requires 20 machine hours of production time and each ton of Y requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. The entire firm's output can be sold and profit made is 80 R.O of X and 120 R.O per ton of Y. It is required to determine the production schedule for maximum profit and to calculate this profit. Formulate a LPP.46. Ford is going to produce a new vehicle, the Pioneer,and wants to determine the amount of annual capacityit should build. Ford’s goal is to maximize the profitfrom this vehicle over the next five years. Each vehicle will sell for $19,000 and incur a variable production cost of $16,000. Building one unit of annual capacity will cost $2000. Each unit of capacity will alsocost $1000 per year to maintain, even if the capacityis unused. Demand for the Pioneer is unknown butmarketing estimates the distribution of annual demandto be as shown in the file P09_46.xlsx. Assume thatthe number of units sold during a year is the minimumof capacity and annual demand. Which capacity levelshould Ford choose? Do you think EMV is the appropriate criterion?Brady Corporation produces cabinets. Each week, itrequires 90,000 cu ft of processed lumber. The companymay obtain lumber in two ways. First, it may purchaselumber from an outside supplier and then dry it in thesupplier’s kiln. Second, it may chop down logs on its ownland, cut them into lumber at its sawmill, and finally dry thelumber in its own kiln. Brady can purchase grade 1 or grade2 lumber. Grade 1 lumber costs $3 per cu ft and when driedyields 0.7 cu ft of useful lumber. Grade 2 lumber costs $7per cubic foot and when dried yields 0.9 cu ft of usefullumber. It costs the company $3 to chop down a log. Afterbeing cut and dried, a log yields 0.8 cu ft of lumber. Bradyincurs costs of $4 per cu ft of lumber dried. It costs $2.50per cu ft of logs sent through the sawmill. Each week, thesawmill can process up to 35,000 cu ft of lumber. Eachweek, up to 40,000 cu ft of grade 1 lumber and up to 60,000cu ft of grade 2 lumber can be purchased. Each week, 40hours of time are available for…
- A manager must make a decision on shipping. There are two shippers, A and B. Both offer a twoday rate: A for $500 and B for $525. In addition, A offers a three-day rate of $460 and a nine-dayrate of $400, and B offers a four-day rate of $450 and a seven-day rate of $410. Annual holdingcosts are 35 percent of unit price. Three hundred boxes are to be shipped, and each box has a priceof $140. Which shipping alternative would you recommend? Explain.A manufacturer produces two types of calculator; each requiring material and labour as shown below: Input Scientific Calculator Graphic Calculator Availability Labour (hrs) 4 5 200 Inspection time 2 1 80 Material (cm2) 10 12 600 PROFIT $200 $300 Write the objective function and he constraints Diagram the constraint and identify the feasible region Using the corner point method, identify the production level that meets the objective of maximum profit1. Cox Electric makes electronic components and has estimated the following for a new design of one of its products. Fixed cost = $24,375 Material cost per unit = $0.17 Labor cost per unit = $0.12 Revenue per unit = $0.68 Note that fixed cost is incurred regardless of the amount produced. Per-unit material and labor cost together make up the variable cost per unit. Assuming that Cox Electric sells all that it produces, profit is calculated by subtracting the fixed cost and total variable cost from total revenue. Construct an appropriate spreadsheet model to find the profit based on a given production level and use the spreadsheet model to answer these questions. a. Construct a one-way data table with production volume as the column input and profit as the output. Breakeven occurs when profit goes from a negative to a positive value; that is, breakeven is when total revenue = the total cost, yielding a profit of zero. Vary production volume from 0 to 100,000 in increments of 10,000.…