A company produces three products, X, Y, and Z. Each unit of Product X requires 2 hours of labor, 1 hourof machine time, and 3 hours of assembly time. Each unit of Product Y requires 1 hour of labor, 2 hours ofmachine time, and 2 hours of assembly time. Each unit of Product Z requires 3 hours of labor, 2 hours ofmachine time, and 1 hour of assembly time.The company has the following resources available: 200 hours of labor, 150 hours of machine time, 120hours of assembly timeThe profit per unit for each product is as follows: Product X: Rs. 30/-, Product Y: Rs, 25/-, Product Z: Rs.20/-. The company wants to maximize its total profit.a)b)d)Note: s1, s2and s3 relates to products X, Y, and Z respectively.Quantity2YXBasicVariables4152-62(111)(iv)Formulate a linear programming model for the above problem.Prepare the first simplex table.Find the pivot element.(vi)As per the above table;(1)(ii)(vii)The final simplex table for the above problem is given below.(ix)(x)1813.636430X53.6364 015.4545 011.8182 130025y01025020Z1002000S₁0$₂0.36360.0909-0.45450.63640.1818-0.45451.36364.0909-1.3636 -4.0909What is the optimal solution?Interpret the shadow prices of labor hours, machine hours, and assembly hours.Construct the dual for the problem.Find the optimal values for the dual variables.0S3-0.27270.09090.36367.7273-1.7273Find the range within which the production of X can be changed without affecting the optimalsolutionFind the range within which the production of Y can be changed without affecting the optimalsolution(viii) Identify the range within which labor hours can be varied without altering the optimalsolution.Find the range within which the production of Z can be changed without affecting the optimalsolutionIdentify the range within which machine hours can be varied without altering the optimalsolution.Identify the range within which assembly hours can be varied without altering the optimalsolution.

Let me state the given data, Product XProduct YProduct ZProfit per unit302520ConstraintsProduct…

Answered: a) b) c) Formulate a linear programming…

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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A diabetic patient needs at least 40 units of Vit. A, at least 30 units of Vit. C, and atleast 30 units of Vit. E each day. Each brand X multivitamin capsule contains 4 units of Vit. A, 6 units of Vit. C, and 2 units of Vit. E; each brand Y capsule contains 5 units of Vit.A, 3 units of Vit.C, and 5 units of Vit. E. If each brand X capsule costs P6.00 and eachbrand Y capsule costs P9.00, how many capsules should the patient take each day tominimize the costs? Solve using graphical method. Show complete solution.
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a) b) c) Formulate a linear programming model for the above problem. Prepare the first simplex table. Find the pivot element.