Suppose the following function is a model for the profit of a certain firm producing boxes of chocolates $(5$ points$*4=20$ points$)$

$(Q)=-2Q^2+40Q$

a$.$ Work out the quantity that maximizes this profit.

b$.$ Work out the quantity that breaks even this firm by hand.

c$.$ Work out the quantity that breaks even this firm using spreadsheet modeling $($note that $Q>0).$

d$.$ Work out the quantity that breaks even this firm using Excel Solver $($note that $Q>0).$