In a manufacturing facility production manager is using EOQ model to calculate the optimum lot

sizes for a product with annual demand rate of $D,$ holding cost $h$ and production set$-$up $costA.$ The

production manager realizes that he is making by ignoring finiteness of production rate.

a$.$ How much change would the manager observe in the maximum amount of inventory when he

starts using a finite$-$production rate model? Give percent change of maximum inventory level in

terms of problem parameters.

b$.$ Write the optimum cost equation of the finite$-$production rate model and show that the optimum

cost is decreasing in $A.$

c$.$ The manager is challenged to make an economic feasibility analysis for an investment that

decreases the setup cost from $A$ to $A^{\text{'}}=nA.$ The investment cost function is estimated to be $C(n)=$

$C_0+n^{},$ where $0.$ What is the optimum capacity investment level, $n^{**},$ if $>1?$