certain nutritional requirements. The liver flavored biscuits contain $1$ unit of nutrient A and $2$ units of nutrient $B$; the chicken flavored biscuits contain $1$ unit of nutrient A and $4$ units of nutrient $B.$ According to federal requirements, there must be at least $40$ units of nutrient A and $60$ units of nutrient $B$ in a package of the new mix. In addition, the company has decided that there can be no more than $18$ liver flavored biscuits in a package. It costs $1$ to make $1$ liver flavored biscuit and $2$ to make $1$ chicken flavored. Doug wants to determine the optimal product mix for a package of the biscuits to minimize the firm's cost.

The L$.$P$.$ Model for Doug to determine the optimal solution is:

Variables:

$x=$ number of liver flavored biscuit in a package

$Y=$ number of chicken flavored biscuit in a package

a$)$ Objective Function: Z$.$