The optimal solution of this linear programming problem is at the intersection of constraints 1 and 2.Max 3x1 + x2s.t. 4x1 + x2≤400 4x1 + 3x2≤600 x1 + 2x2≤300 x1, x2≥0Over what range can the coefficient of x1 vary before the current solution is no longer optimal? (Round your answers to two decimal places.)Compute the dual value for the third constraint.

The coefficient of x1 can vary within the range where the objective function coefficient is between…

Answered: The optimal solution of this linear…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter3: Introduction To Optimization Modeling

Section: Chapter Questions

Problem 50P

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The optimal solution of this linear programming problem is at the intersection of constraints 1 and 2.

Max 3x₁ + x₂

s.t.
	4x₁ + x₂	≤	400
	4x₁ + 3x₂	≤	600
	x₁ + 2x₂	≤	300
	x₁, x₂	≥	0

Over what range can the coefficient of x₁ vary before the current solution is no longer optimal? (Round your answers to two decimal places.)

Compute the dual value for the third constraint.

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This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.

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