b) If the profit per unit of product 2 increased by GHC 2 to GHC 22, would theoptimal productionquantities of products 2 and 3 change? Would the optimal value of theobjective function change?c) If the available amount of material increased by 10 pounds to 210 pounds, howwould that affect the optimal value of the objective functiond) Which resource(s) is/are efficiently used at the optimal? Justify Question 1The linear programming model below was solved by computerМаximize Z 3D 5х, + 20х2 + 14xзSubject to:Labour 5x1 + 6x2+ 4x3 < 210 hoursMachine 4x1 + 2x2 + 5x3< 170 minutesMaterial 10x,+8x2+ 5x3< 200 poundsX1,X2,X3 2 0where x1 = quantity of product 1X2 = quantity of product 2X3 = quantity of product 3The following information was obtained from the output.Total profit = 548.00Variablevalue Reduced costRange of OptimalityProduct 110.6unlimited to 25.60Product 2 59.40 to22.40Product 33212.50 to50.00Constraint Slack Shadow priceRange of FeasibilityLabour520.0158.00 to unlimitedMaterial2.4170.00 to 270.91Machine0.450.00 to 200.0a) By how much would the profit per unit of product 1 have to increase in orderfor it to have a none-zero value?

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Answered: b) If the profit per unit of product 2…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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It is summertime and your winter coat factory is trying to decide its production schedule and staffing level for the next season. You are forecasting a demand of 5000 coats in October, 8000 coats in November, 8000 coats in December, 12000 coats in January, 12000 coats in February, and 9000 coats in March. You want to manufacture these coats at the lowest cost possible/ The first decision you need to make is how many people to hire. Each employee will cost $2500 a month. You don’t want to hire or fire any employees mid-season in order to minimize disruptions in your factory floor. You can have employees idle if there isn’t sufficient work for them to do. Employees still need to be paid even if they are idle. An employee works 20 business days a month and takes half a day to produce one coat. The employees can also be asked to work overtime, in which case you need to pay them $70 per coat they produce. You don’t need to assume there is any capacity constraint on the number of overtime…
A small candy shop is preparing for the holiday season. The owner must decide how many bags of deluxe mix and how many bags of standard mix of Peanut/Raisin Delite to put up. The deluxe mix has 2/3 pound raisins and 1/3 pound peanuts, and the standard mix has pound raisins and ½ pound peanuts per bag. The shop has 90 pounds of raisins and 60 pounds of peanuts to work with. Peanuts cost $0.60 per pound and raisins cost $1.5 per pound. The deluxe mix will sell for $2.90 per pound, and the standard mix will sell for $2.55 per pound. The owner estimates that no more than 110 bags of one type can be sold. Using Simplex method a. If the goal is to maximize profits, how many bags of each types should be prepared? b. What is the expected profit?
A company produces a niche hunting blind. Because of the nature of this product, demand varies greatly by season. In fact, demand exceeds production capacity during hunting season (fall,) but is very low in the summer months. To meet the high demand during the fall, the company produces the blind year round, producing more than what is needed in the summer in order to carry over inventory into the peak season. Their production facility can produce at most 60 blinds per month using regular labor at a cost of $125 each. Up to 15 additional blinds can be produced by utilizing overtime labor at a cost of $135 each. The blinds are sold for $225. Because of storage cost and the opportunity cost of capital, each blind held in inventory from one month to the next incurs a cost of $15 per blind. Since demand is uncertain, the company would like to maintain an ending inventory of at least 5 blinds during the warm months (May–September) and at least 15 blinds during the other months…
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Afresh food company in Oman is specialized in apples distribution in Oman. Annual sales forecast is 4800 boxes of apple. It costs OR 50 to make and receive an order and holding cost is OR 3.5 per box per year. The prices depend on quantities purchased such that the order quantities (in boxes) from 1 to 199 at a unit price RO 5; quantity 200 to 499 at a unit price 4.5 RO; and quantity 500 and more at a per unit price of 4 RO. If the discount option is considered, then the best order quantity that minimizes the total annual inventory cost is O a. None is correct O b. 200 O c. 199 O d. 371 O e. 500
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1
solve the LP Models asap
A small candy shop is preparing for the holiday season. The owner must decide how many bags of deluxe mix and how many bags of standard mix of Peanut/Raisin Delite to put up. The deluxe mix has 2/3 pound raisins and 1/3 pound peanuts, and the standard mix has 1/2 pound raisins and 1/2 pound peanuts per bag. The shop has 90 pounds of raisins and 60 pounds of peanuts to work with. Peanuts cost $.60 per pound and raisins cost $1.50 per pound. The deluxe mix will sell for $4.00 for a one-pound bag, and the standard mix will sell for $3.55 for a one-pound bag. The owner estimates that no more than 210 bags of one type can be sold. a. If the goal is to maximize profits, how many bags of each type should be prepared? Deluxe _____bags Standard ______bags b. What is the expected profit? Profit ________
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