Problem $1$ A retailer sells a perishable commodity and each day he places an order for $Q$ units. Each unit that is sold gives a profit of $60$ cents and units not sold at the end of the day are discarded at a loss of $40$ cents per unit. The demand, $D,$ on any given day is uniformly distributed over $80,140.$ How many units should the retailer order to maximize expected profit?

Problem $2$ Redo Problem $1$ numerically using MATLAB and compare the results.