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?

Answered: Image /qna-images/answer/a3e94f1b-b3a4-4d88-940a-043d538529e1.jpg

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.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 56P

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Q-1)A glass melting furnaces feed auto plumping machines for producing the electric lamp casing (balloon),there are two main kinds can be produced, the original and the big one, they must produce at least 25 million of the original but not accede over 35 million ,and they must produce 3 million of the big one, however the ratio of the original must be at least 5 times to the big one which make a profit double the original, producing million of the big one utilize 5% Of the available materials but the original utilize 2.5% of the available materials ,For this problem ,the objective function is: Max Z =0.5X1+2X2 O MIN Z =2X1+X2 O Max Z =2X1+2X2 O Max Z =2X1+X2
Q: Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$5 consider Cake (C) 0 -0.5 4.5 0.5 1E+30 $C$5 consider Dozen Cookies (D) 10 0 10 1E+30 1 what does the value minus .5 for the reduced cost of C mean (other than it is the change in thevalue of the coefficient in the objective function so that the solution includes a positive amountof C)?
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Ex 4.12 Formulate the linear programming model of the following problems. Titan Credit Card Marketing works for HSBC to verify and approve credit card application. TCCM receives P380 for every completed customer application. The company maintained three call agents targeting at P20,000 worth of approvals daily, altogether. In a regular working day, James can process as much as P3000 worth of applications. Mark can process twice as much as Tim. How many credit cards should each call agent process to achieve the target for the day. Formulate the LP model
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Q1. Explain the SPACE Matrix in detail with suitable examples

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