$24.$ Mr$.$ Meadows Cookie Company makes a variety of chocolate chip cookies in

the plant in Albion, Michigan. Based on orders received and forecasts of buying habits, it is estimated that the demand for the next four months is $850,$

Table $31$ Aggregate Plan for Densepack Obtained from Rounding the Linear Programming Solution

A B C D E F G H I

Number

Number of Units Ending

Number of Number Number of Units Produced Cumulative Cumulative Inventory

Month Workers Hired Fired per Worker $($B$3$ E$)$ Production Net Demand $($G $2$ H$)$

January $273272\mathrm{.}93180080078020$

February $2733\mathrm{.}5179601,7601,420340$

March $2732\mathrm{.}6387202,4802,320160$

April $2733\mathrm{.}8101,0403,5203,5200$

May $7384653\mathrm{.}2242,3795,8995,520379$

June $7382\mathrm{.}1981,6227,5217,5201$

Totals $46527900$

$3\mathrm{.}5$ Solving Aggregate Planning Problems $155$

$1,260,510,$ and $980,$ expressed in thousands of cookies. During a $46-$day

period when there were $120$ workers, the company produced $1\mathrm{.}7$ million cookies. Assume that the number of workdays over the four months are respectively

$26,24,20,$ and $16.$ There are currently $100$ workers employed, and there is no

starting inventory of cookies.

a$.$ What is the minimum constant workforce required to meet demand over the

next four months?

b$.$ Assume that cI $510$ cents per cookie per month, cH $5$ $$100,$ and cF $5$ $$200.$

Evaluate the cost of the plan derived in part $($a$).$

c$.$ Formulate as a linear program. Be sure to define all variables and include the

required constraints.

d$.$ Solve for the optimal solution