Determine the minimum constant workforce plan for Paris Paint and the cost of the plan.

Assume that stock$-$outs are not allowed.

b$)$ If Paris were able to back$-$order excess demand at a cost of $$2$ per gallon per quarter, determine

a minimum constant workforce plan that holds less inventory than the plan you found in part

$($a$),$ but incurs stock$-$outs in quarter $2.$ Determine the cost of the new plan.

c$)$ Formulate this as a linear program. Assume that stock$-$outs are not allowed.

d$)$ Solve the linear program. Round the variables and determine the cost of the resulting plan