4. Each year, Holly's Best Salad Dressing, Inc. (HBSD) purchases 50,000 gallons of extra virgin olive oil. Ordering costs are $100 per order, and the carrying cost, as a percentage of inventory value, is 80 percent. The purchase price to HBSD is $0.50 per gallon. Management currently orders the EOQ each time an order is placed. No safety stock is carried. The supplier is now offering a quantity discount of $0.03 per gallon if HBSD orders 10,000 gallons at a time. Should HBSD take the discount?

HBSD should take the discount because it will

lead to as savings of  $1,120.00  

Explanation:

step 1

Determine the the inventory cost of EOQ

EOQ =√ (2× Co× D)/Ch

= √(2× 100× 50,000)/ 80% × $0.50

= 5,000 units

Inventory cost = Purchase cost + Ordering cost + carrying cost

                                                                     $

Purchase cost = 50,000 × $0.50   =   25,000.00

Ordering cost   = (50,000/5000)× 100  = 1,000

carrying cost  =  (5000/2) × $0.50 × 80% = 1,000

Total cost                                                   27,000.

Step 2

Determine the inventory cost for order of 10,000 gallons

Order of 10,000 gallons

Purchase cost = $(0.50-0.03) × 50,000      = 23,500.

Ordering cost = (50,000/10,000) × 100   =          500

Carrying cost = (10000/2) × $(0.50-0.03)× 80%  =1880

Total cost                                                             25,880.

Step 3

Compare the cost under the two options

HBSD should take the discount because it will

lead to as savings of  $1,120.00   i.e (927,000 - 25,880.)

start by isolating the variable on one side by adding 43w^2 to both sides.   the equation will read:

25w^2+5=0

*subtract 5 from both sides*

25w^2=-5

*divide both sides by 25*

w^2=-1/5

*take the square root of both sides*

w=√(-1/5)

the square root of -1 is i.   the square root of 5 remains √5

the answer is i/√5.

hope this