Managment Science problem Step 1: Find the slope of the objective function. Step

Question

Managment Science problem

Step 1: Find the slope of the objective function.

Step 2: Substitute an arbitrary coefficient for the coefficient of x2 in the objective function and find the slope

Step 3: Find the slope of the labor constraint and set it equal to the slope of the objective function found in step 2.

Step 4: Find the slope of the clay constraint and set it equal to the slope of the objective function found in step 2. Step 5: Express and interpret the complete sensitivity range for the coefficient of x2 in the objective functions.

Explanation / Answer

Step 1: slope of objective function. Let z = 0, So objective function equation implies, x2 = - 4/3x1

Therefore slop of objective function = - 4/3

Step 2: Let the arbitrary coefficient of x2 be 50, So objective function equation implies, x2 = - 4/5x1

Therefore slop of objective function = - 4/5

Step 3: Slope of Labor constraint (2/5x1 + 1/2x2 20) , slope = - 4/5

This is already equal to the slope of objective function as calculated in step 2.

Step 4: Slope of Clay constraint (3/5x1 + 3/10x2 21) , slope = -2

Setting the slope of clay constraint equal to - 4/5, the constraint changes to 4/5x1 + x2 21

Step 5: From step 3 and 4, we see that the sensitivity range for the coefficient X2 in the objective function is the range from slop of labor constraint and clay constraint. So the sensitivity range is from 50 (this results in slope = -4/5) to 20 (slope = -2).

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