Problem: Consider the following LP application problem:
A company makes three types of candy and packages them in three assortments. Assortment I contains 4 sour, 4 lemon, and 12 lime candies, and sells for $9.40. Assortment II contains 12 sour, 4 lemon, and 4 lime candies, and sells for $7.60. Assortment III contains 8 sour, 8 lemon, and 8 lime candies, and sells for $ 11.00. Manufacturing costs per piece of candy are $0.20 for sour, $0.25 for lemon, and $ 0.30 for lime. They can make 5,200 sour, 3,800 lemon, and 6,000 lime candies weekly. How many boxes of each type should the company produce each week in order to maximize its profit? What is the maximum profit? Respond in a comprehensive manner to each the following questions:
a. Can this application be solved graphically in an (x, y) coordinate plane? Explain.
b. Formulate and state the objective function for this application problem.
c. Will the constraints in this application problem be linear?
d. Will a feasible 2-D solution space exist in the above model that allows for the determination of the optimal solution?