Problem 3 - Sensitivity(15\%). Mike's smoothie cart has 4 different products or blends that it sells. He has assembled the linear program to maximize profit. He is constrained by his smoothie ingredients, his time (labor), by a minimum number of mix 2 and mix 3 that he must sell to keep the city health inspectors happy in order to remain in business, and by a total minimum number of blends that he must make to keep encouraging customers to show up. Use the output to his linear program and the sensitivity repot to answer the questions on the following page. How many of each smoothie should be produced to maximize profit? What is the maximum profit attainable while satisfying all of the constraints? Which of the following constraints have slack or surplus? If a single constraint was added to the problem to assure that at least three times as many of "Mix 1" smoothies were blended and sold than "Mix 2 " smoothies, what would happen to the objective function value ("Increase" / "Decrease" / "No Change" / "Don't Know")? If a single constraint was added to the problem to assure that there must be at most 8 "Mix 3 " smoothies blended and sold, could the objective function value become more optimal ("Yes" / "No")? If the company could obtain additional blueberries, what is the maximum number of additional blueberries that should be obtained? Using your answer from the above question, what would be the new optimal profit from the model if the maximum number of blueberries is obtained? What is the highest profit margin that the company could receive from "Mix 1p and still retain the same optimal solution? What is the lowest profit margin that the company could receive from "Mix 4n and still retain the same optimal solution? Use the picture for reference. If the optimal solution was 3.0, 5.0. 8.0, and 8.0 (it is not, but assume it is and assume it is a feasible solution) for Mix 1, Mix 2, Mix 3 , and Mix 4 respectively, what would be the LHS value for the yogurt constraint