Question: Q3: Consider a profit maximisation problem constrained by availability of labor and material that has been formulated as the linear program given below: max s.t.

Q3: Consider a profit maximisation problem

Q3: Consider a profit maximisation problem constrained by availability of labor and material that has been formulated as the linear program given below: max s.t. p= 10.21 +8.22 11 + 3.22 0. (labour) (material) (a) Solve the above LP by any valid method (including the use of software). (b) What are the shadow prices of labor and material obtained from the given tableau? What is their interpretation? (c) Suppose the availability of labor changed from 30 to 30 + A. Determine the range of values of A for which the same variables remain in the optimal tableau. (d) Suppose now that the availability of labor changes from 30 to 130 (that is A = 100). Find an optimal solution. (e) Suppose that the profit coefficient of 22 changed from 8 to 8+ A. Determine the range of values of A for which the same variables remain in the optimal tableau. [15 marks]

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