A manufacturer of industrial seafood processing equipment wants you to develop an aggregate plan for the four quarters of the upcoming year using the following data on demand and capacity.

\begin{array}{|l|l|l|l|l|l|}\hline&&\text { Regular}&\text { Over- }&\text { Sub- }&\text { Initial inventory } &250 \text { units }\\\text { Quarter }&\text { Units}&\text { Time }&\text { Time }&\text { contract }&\text { Regular time cost } &\$ 1.25 \text { /unit }\\\hline1&200&400&80&100& \text { Overtime cost } & \$ 1.50 / \text { unit } \\\hline 2&750&400&80&100&\text { Subcontracting } & \\&&&&&\text { cost } & 2.00 / \text { unit } \\\hline3&1200&800&160&100& \text { Carrying cost } & \$ 0.50 / \text { unit/quarter }\\\hline &&&&&\text { No back ordering } & \\4&450&400&80&100&\text { is allowed } &\\\hline \end{array}

a. Find the optimal plan using the transportation method.
b. What is the cost of the plan?
c. Does any regular time capacity go unused?
How much in what periods?
d. What capacity went unused in this solution (list in detail)?

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