Question $1$: $15$ points

The plastics purchasing team needs to determine the optimum ordering strategy for their plastic purchases to make the wide variety of plastic parts that go into various products. They order from their supplier on a weekly basis. The supplier will give them a $15\%$ discount on any amount over $2,000lbs.($the $2,000lb.$ cost will not change, just the amount above $2,000.)$ The following table describes the demand and costs per $lb.$ before the discount.

$\backslash$table$[[,$Week $1,$Week $2,$Week $3,$Week $4,$Week $5],[$Demand $($lbs$.),2,665,2,914,1,200,1,535,3,957],[$Before discount cost per lb$.,$$$8\mathrm{.}20,$$$10\mathrm{.}20,$$$6\mathrm{.}30,$$$7\mathrm{.}10,$$$10\mathrm{.}50$