Question

Sunshine Motors is a large car dealership. Its most popular car is a 4-wheel drive, sport utility vehicle. The new year models are available and the dealer must determine how many of these vehicles to order from the car manufacturer. Demand is estimated at 160 vehicles per year. The annual carrying cost is $650 per car and the ordering cost is $700 per order. Determine the optimal order size, total annual inventory cost and the order cycle time

Answer 1

the optimal order size Q is 18.56 cars

the annual inventory cost = $12066.48

the order cycle time is 42.34 days

Step-by-step explanation:

Using the following expression to determine the optimal order size Q:

`Q = \sqrt{(2* ordering \ cost \ * Demand)/(Annual \ carrying \ cost )}`

`Q = \sqrt{(2* 700 * 160)/(650 )}`

`Q =√(344.6153846)`

`Q = 18.56`

Hence; the optimal order size Q is 18.56 cars

The annual inventory cost is mathematically expressed as:

`(ordering \ cost * Demand)/(optimal \ order \ size) + (annual \ carrying \ cost)/(2)`

=
`(700*160)/(18.56) +(650*18.56)/(2)`

= 6034.482759 + 6032

= $12066.48276

≅ $12066.48

Hence, the annual inventory cost = $12066.48

For The order cycle time; we have;

Order cycle time =
`(365 \ days )/(1) / ( ( Demand )/(optimal \ order \ time ))`

=
`(365 )/(1) / ((160 )/(18.56))`

=
`(365 )/(1) / (8.62)`

=
`(365 )/(1) * (1)/( 8.62)`

= 42.34 days

Hence, the order cycle time is 42.34 days