$13.$ Rapid Grower, the supplier of plant food for Greens in Problem $12,$ has offered the following quantity discounts. If the nursery places orders of $60$ bags or less, the cost per bag is $$25.$ For orders of $60$ to $100$ bags, the cost per bag is $$23.$ For orders over$100$ bags, the cost is $$22$ per bag. Greens estimates its holding cost to be $25$ percent of the unit price. Determine the most cost$-$effective ordering policy for Greens.

EOQ$$at$$price$$of$$$$22/$bag

$=$

$2$

$($

$1780$

$)$

$($

$12$

$)$

$22$

$($

$0\mathrm{.}25$

$)$

$=$

$88$

$$

bags

$$

$($

infeasible$$quantity

$)$

EOQ$$at$$price$$of$$$$23/$bag

$=$

$2$

$($

$1780$

$)$

$($

$12$

$)$

$23$

$($

$0\mathrm{.}25$

$)$

$=$

$86$

$$

bags

$$

$($

feasible$$quantity

$)$

EOQ$$at$$price$$of$$$$25/$bag

$=$

$2$

$($

$1780$

$)$

$($

$12$

$)$

$25$

$($

$0\mathrm{.}25$

$)$

$=$

$83$

$$

bags

$$

$($

infeasible$$quantity

$)$

Total cost at feasible EOQ amount$=(86/2)(23\backslash$times $0\mathrm{.}25)+(1780/86)(12)+(23)(1780)=$$$41,435\mathrm{.}62$

Total cost at Q$=100$: $(100/2)(23\backslash$times $0\mathrm{.}25)+(1780/100)(12)+(23)(1780)=$$$41,441\mathrm{.}10$

Optimal ordering policy is to order $86$ bags at a time.

$14.$ In an effort to reduce its inventory, Rapid Grower is offering Greens, a local nursery $($Problems $12$ and $13),$ two additional price breaks to consider. If the nursery orders a three$-$month supply, the cost per bag is $$16.$ If Greens orders a six$-$month supply, the cost per bag is $$14\mathrm{.}50.$ Should Greens change its order quantity calculated in Problem $13?$