The Meredith Ribbon Company produces paper and fabric decorative ribbon which it sells to paper products companies and craft stores.The demand for ribbon is seasonal.Information about projected demand and production for a particular type of ribbon is given.

\begin{array} { l c c c } & \text { Demand (yards) } & \text { Froduction Cost Per Yard } & \text { Froduction Capacity (yards) } \\\hline \text { Quarter 1 } & 10,000 & .03 & 30,000 \\\text { Quarter 2 } & 18,000 & .04 & 20,000 \\\text { Quarter 3 } & 16,000 & .06 & 20,000 \\\text { Quarter 4 } & 30,000 & .08 & 15,000\end{array}

An inventory holding cost of $.005 is levied on every yard of ribbon carried over from one quarter to the next.
a.Define the decision variables needed to model this problem.
b.The objective is to minimize total cost,the sum of production and inventory holding cost.Give the objection function.
c.Write the production capacity constraints.
d.Write the constraints that balance inventory,production,and demand for each quarter.Assume there is no beginning inventory in quarter 1.
e.To attempt to balance the production and avoid large changes in the workforce,production in period 1 must be within 5000 yards of production in period 2.Write this constraint.

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