Provide an appropriate response.A store makes two different types of smoothies by blending different fruit juices. Each bottle of Orange Daze smoothie contains 10 fluid ounces of orange juice, 4 fluid ounces of pineapple juice, and 2 fluid ounces of blueberry juice. Each bottle of Pineapple Blue smoothie contains 5 fluid ounces of orange juice, 6 fluid ounces of pineapple juice, and 4 fluid ounces of blueberry juice. The store has 500 fluid ounces of orange juice, 360 fluid ounces of pineapple juice, and 250 fluid ounces of blueberry juice available to put into its smoothies. The store makes a profit of $1.50 on each bottle of Orange Daze and $1 on each bottle of Pineapple Blue. To determine the maximum profit, the simplex method can be used and the final tableau is: x1 x2

Question

x3  x4  x5  M   Give an interpretation to the fact that the marginal value of blueberry juice is zero. Refer in your explanation to the value in the final tableau of the slack variable x5.



What will be an ideal response?

Answer 1

The slack variable x5 which corresponds to the blueberry juice constraint has value 30 in the optimal solution. This means that not all the available blueberry juice is used, so there is no increase in profit if the amount of blueberry juice is increased. Hence the marginal value of blueberry juice is zero.