A company has three factories. Each factory produces three different products (A, B and C). Factory 1 has a daily production capacity production of 8 units of A, 4 units of B and 8 units of C. Factory 2 has a daily production capacity of 6 units of A, 6 units of B and 3 units of C. Factory 3 has a production capacity of 12 units of A, 4 units of B and 8 units of C. The total demand for product A is 300 units, for product B is 172 units and for product C is 250 units. The daily operating cost for Factory 1 is $55 for Factory 2 is $60 and for Factory 3 is $50. How many days should each factory be operated in order to fill the total demand and the keep the operating cost at a minimum? (i) Show a model that represents the company's problem. (ii) Write down the dual maximization problem. (iii) Write down the initial simplex tableau. (iv) Identify the entering, departing and pivot variables. (v) Use the simplex method to determine the optimal tableau. Ensure that you explain each step in the computation. (vi) Identify the basic and non-basic variables. (vii) Identify the optimal solution.

A company has three factories. Each factory produces three different products (A, B and C). Factory 1 has a daily production capacity production of 8 units of A, 4 units of B and 8 units of C. Factory 2 has a daily production capacity of 6 units of A, 6 units of B and 3 units of C. Factory 3 has a production capacity of 12 units of A, 4 units of B and 8 units of C. The total demand for product A is 300 units, for product B is 172 units and for product C is 250 units. The daily operating cost for Factory 1 is $55 for Factory 2 is $60 and for Factory 3 is $50. How many days should each factory be operated in order to fill the total demand and the keep the operating cost at a minimum? (i) Show a model that represents the company's problem. (ii) Write down the dual maximization problem. (iii) Write down the initial simplex tableau. (iv) Identify the entering, departing and pivot variables. (v) Use the simplex method to determine the optimal tableau. Ensure that you explain each step in the computation. (vi) Identify the basic and non-basic variables. (vii) Identify the optimal solution.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 54P

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