Consider the following table:

Demand $($in units$)151617181920212223242526272829$

Probability $0\mathrm{.}010\mathrm{.}020\mathrm{.}030\mathrm{.}050\mathrm{.}070\mathrm{.}10\mathrm{.}120\mathrm{.}120\mathrm{.}110\mathrm{.}090\mathrm{.}090\mathrm{.}080\mathrm{.}060\mathrm{.}040\mathrm{.}01$

Cost per unit: $25$

Selling price per unit: $75$

Scrap value per unit: $12$

Handling cost of handling scrap: $5$

What is the expected profit if the stock is $20$ units, considering the costs of understocking and overstocking?