A produce company supplies organically grown apples to four regional specialty stores. After the apples are collected at the company’s orchard, they are transported to any of three preparation centers where they are prepared for retail (by undergoing extensive cleaning and then packaging). After the apples are prepared, they are shipped to the specialty stores. Due to the fragility of the product, the cost of transporting this organic fruit is rather high. The company has three preparation centers available for use. The Apple worksheet contains: (i) the unit preparation costs (in $/pound) to get the apples from company’s orchard to the preparation centers and then prepare the apples for retail, (ii) the preparation centers’ monthly capacities, (iii) the demand at the specialty stores, and (iv) the unit costs of transporting the apples from the preparation centers to the specialty stores.
a. Construct and solve a linear optimization model to determine the number of pounds of apples to prepare at each of the three preparation centers and how much of each specialty store’s demand to supply from each preparation center, to minimize the total cost of the operation.
b. In a separate worksheet, reformulate the problem to determine if there is an alternative optimal solution. Clearly explain your result.