Suppose we want to choose capacity for a plant that will produce a new drug. In particular, we want to choose the capacity that maximizes discounted expected profit over the next $10$ years. We have the following information:

$*$ Demand for the drug is expected to be normally distributed ~ Normal $(50,000,12,000).$

$*$ A unit of capacity costs $$16$ to build.

$*$ The number of units produced will equal the demand, up to capacity limits$.$

$*$ The revenue per unit is $$3\mathrm{.}70$ and the cost per unit is $$0\mathrm{.}20($variable cost$).$

$*$ The maintenance cost per unit of capacity is $$0\mathrm{.}40($fixed cost$).$

$*$ The discount rate is $10\%.$

Perform a simulation assuming the plant will be designed to meet the expected demand $($i$.$e$.,50,000$ units$).$ You may use the template below to build your model: