equipment, capacity, and so on$.$ The Dayton plant has weekly costs that can be expressed as a function of the number of gloves produced

$TCD(x)=x^2-x+6$

$TCH(Y)=Y^2+2Y+2$

possible cost.

$($a$)$ Formulate a mathematical model that can be used to determine the optimal number of gloves to produce each week at each facility.

min,

$s.t.x+Y=9$

$,x,Y0$

dollars$)?$

$$,$ at $(x,Y)=(,)$