Question

Foods Galore is a major distributor to restaurants and other institutional food users. Foods Galore buys cereal from a manufacturer for $20.00 per case. Annual demand for cereal is 200,000 cases, and the company believes that the demand is constant at 800 cases per day for each of the 250 days per year that it is open for business. Average lead time from the supplier for replenishment orders is eight days, and the company believes that it is also constant. The purchasing agent at Foods Galore believes that annual inventory carrying cost is 10 percent and that it costs $40.00 to place an order.

How many cases of cereal should Foods Galore order each time it places an order? What is the total annual inventory cost if you order based on your Economic Order Quantity? (Sum of annual product purchasing cost, holding cost, and ordering cost). What is the total annual inventory cost if Foods Galore orders 10,000 each order at $18 per case? (Sum of annual product purchasing cost, holding cost, and ordering cost)

Answer 1

The appropriate solution is:

(a) 2828 cases each time

(b) $4005656.85

(c) $3609800

Step-by-step explanation:

The given values are:

Annual demand,

D = 200,000 cases

Per case cost,

C = $20

Carrying host,

H =
`10 \ percent* 20`

= $
`2`

Ordering cost,

S = $40

(a)

The economic order quantity will be:

⇒
`Q^*=\sqrt{((2DS)/(H) )}`

On substituting the values, we get

`=\sqrt{[((2* 200000* 40))/(2) ]}`

`=\sqrt{(16000000)/(2) }`

`=2828`

(b)

According to the question,

The annual ordering cost will be:

=
`((D)/(Q^*)) S`

=
`((200000)/(2828)) 40`

=
`2828.85` ($)

The annual carrying cost will be:

=
`((Q^*)/(2))H`

=
`((2828)/(2) )2`

=
`2828` ($)

The annual purchase cost will be:

=
`D* C`

=
`200000* 20`

=
`4000000` ($)

Now,

The total inventory cost will be:

=
`2828.85+2828+4000000`

=
`4005656.85` ($)

(c)

According to the question,

Order quantity,

Q = 10000 cases

Per case cost,

C = $18

Carrying cost,

H =
`10 \ percent* 18`

=
`1.8`

The annual ordering cost will be:

=
`((D)/(Q) )S`

=
`((200000)/(10000) )40`

=
`800` ($)

The annual carrying cost will be:

=
`((Q)/(2) )H`

=
`((10000)/(2) )1.8`

=
`9000` ($)

The annual purchase cost will be:

=
`D* C`

=
`200000* 18`

=
`3600000`

Now,

The total cost of inventory will be:

=
`800+9000+3600000`

=
`3609800` ($)