Jp Molassas
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JP Molasses
The analysis is divided into three sections:
Part I: description of the optimization model
Part II: solution to the present problem
Part III: recommendations on future improvements to increase profits
Part I
Objective function: J.P. Molasses goal is to maximize the profit generated from the refining of raw sugar into molasses and its byproducts and then shipping those products to customers.

Decision variables:
a. The amount of raw sugar shipped from eight suppliers to two processing plants
b. The amount of molasses and byproduct shipped to seven customers (a majority of which are internal and therefore dont generate profit accounted for in this model).

c. Because these variables represent amount shipped they cannot be negative.
Constraints:
a. Total raw sugar shipped from each supplier to each refinery must be less than or equal to the amount available to ship
b. Total molasses shipped from each refinery to each customer must be equal to the quantity required by that customer.
c. The two processing plants must operate at between 50-100% of capacity
d. The amount of purified sugar produced at the Charleston plant is limited to 2,000,000 pounds per month because of storage constraints
e. Total molasses shipped to customers (including excess) must be less than or equal to the total molasses produced
Part II
There are two solutions that provide the optimal profit given the current constraints under which JP Molasses operates. Under these conditions, the optimal profit is \$63,571. This profit margin is achieved in both cases with revenue of \$942,354 and cost of \$412,333 for material purchased and \$466,450 for fixed and variable costs in processing, for total cost of \$878,783.

This optimal profit can be achieved with two different allocations of raw sugar shipments to processing plants, as below :
\$B\$6 Spectra Charleston 1000 160
\$C\$6 Spectra Atlanta 0 840
\$B\$9 Omega Charleston 530 1370
\$C\$9 Omega Atlanta 840 0
Part III
The binding constraints are the storage capacity in Charleston, the quantities available from the suppliers of raw sugar, and the amount of molasses shipped out to customers from Atlanta. However, the processing capacity constraints at the Charleston and Atlanta plant are not binding. Assuming JP Molasses has the capacity to make some up front investments, we recommend modifying some of these binding constraints to increase annual profits.

Increasing storage capacity for purified sugar would increase profit in the Charleston plant. This constraint of 2,000 Klbs has the highest shadow price (\$62 per Klbs). Charlestons storage capacity could be increased by up to 328.5 Klbs before the set of binding constraints changes. More raw sugar would be processed in Charleston instead of Atlanta,