Question

TexMex Foods operates a plant in Irving, Texas, for manufacturing Taco sauce used in fast food restaurants. The sauce, which is packaged in plastic containers, is made from a special recipe that includes tomato concentrate, onions and chile peppers that TexMex purchases from various suppliers. The plant operates 365 days a year and TexMex uses an annual holding cost rate of 18%. Tomato Concentrate TexMex Foods purchases its tomato concentrate from Hunt farms. The company requires 2500 gallons of concentrate per day to manufacture this sauce. Hunt Farms offers customers the following all units price discount schedule: Number of Gallons Ordered 1 – 9999 10,000 – 49,999 50,000 – 124,999 125,000 – 249,999 250,000 or more Price per Gallon $3.12 $3.08 $3.02 $3.01 $2.96 The shelf life of the concentrate is 80 days, and the ordering cost is $750. Orders must be placed in 1000-gallon increments. The company desires a safety stock of 10,000 gallons, and the lead-time for delivery is 10 days. Management wishes to determine the optimal order quantity for the concentrate as well as the reorder point.

Answer 1

Quantity Discount Schedule

Quantity	Unit Price
1-9999	$3.12
10000-49999	$3.08
50000-124999	$3.02
125000-249999	$3.01
>250000	$2.96

The shelf life = 80 days

Per day consumption = 2500 gallon

Maximum single order quantity = 2500*80=200000

So the last option i.e.>250000 is automatically discarded as it will be more than the quantity for shelf life(200000)

Holding cost = 18% of the purchase cost

Ordering cost = $750

Annual demand = 2500*365= 912500

Slab one: (1-9999)

= 49368 This is not within the range so this is not acceptable

Slab two(10000-49999)

= 49687 this is within the range so it can be accepted

Slab three:(50000-124999)

= 50179 this is within the range This is acceptable

Slab four(125000-249999)

= 50,262 this is not within the range so not acceptable

We got two order size 49687 and 50262 but as the order can be done on 1000 incremental unit the order size should be either 49000 or 50000

the total cost for 49000 order size = 49000*3.08+ (912500/49000)*$750+ (49000/2)*0.18*3.08=150920+13966.83+13582.8=178469.63

The total cost for 50000 order size = 50000*3.02+(912500/50000)*$750+50000/2 * 0.18*3.02=151000+13687.5+13590= 178277.5

So the total cost is less for order size 50000

So the optimal order size should be 50000

Lead time= 10 days

Reorder point = 2500*10 = 25000 units

Please comment if any doubt

rate me

thanks