Question

Sarah’s Organic Soap Company makes organic liquid soap. One of the raw materials for her soaps is organic palm oil. She needs 900 kg of palm oil per day on average. The supplier charges a $57 delivery fee per order (which is independent of the order size) and $5.25 per kg. Sarah’s annual holding cost is 20 percent. Assume she operates and sells five days per week, 52 weeks per year.

Answer 1

5,126, 6,275, 0.026, 9,501

(

(a)

Q* = squareroot((2 x K x R)/h)

K = $60 per order

R = (1,000 x (5 x 52)) = 260,000 per year

h = ($4.75 x .25) = 1.1875 per year

Q* = squareroot((2 x $60 x 260,000)/1.1875)

= squareroot(31,200,000/1.1875)

= squareroot(26,273,684.21)

= 5,125.786204 kgs

(b)

C(Q) = (K x (R/Q)) + ((1/2) x h x Q)

K = $60 per order

R = 260,000 per year

Q = 4,000

h = 1.1875 per year

C(Q=4,000) = ($60 x (260,000/4,000) + ((1/2) x $1.1875 x 4,000)

= $3,900 + $2,375

= $6,275

(c)

C(Q) = (K x (R/Q)) + ((1/2) x h x Q)

K = $60 per order

R = 260,000 per year

Q = 8,000

h = 1.1875 per year

C(Q=8,000) = ($60 x (260,000/8,000)) + ((1/2) x $1.1875 x 8,000)

= $1,950 + $4,750

= $6,700

$6,700/260,000 = $0.025769231

(d)

C(Q) = (K x (R/Q)) + ((1/2) x h x Q)

K = $60 per order

R = 260,000 per year

Q = 15,000 per order

h = ($4.75 - ($4.75 x 0.05)) x 0.25 = 1.128125

C(Q=15,000) = ($60 x (260,000/15,000)) + ((1/2) x 1.128125 x 15,000)

= $1,040 + $8,460.9375

= $9,500.9375

)

Answer 2

$1905

Step-by-step explanation:

Here we will have to calculate Economic Order Quantity to lower the ordering ordering and holding cost as much as we can. So here we will use the following formula to calculate the best number of units that we should order, which is as under:

Economic Order Quantity = SquareRoot (2 * Annual Demand * ordering cost per order / Holding cost per unit per year)

Here

Annual Demand = 900kg of palm oil per day * 52 weeks * 5 day a week / 7

Annual Demand = 900 * 52 * 5 / 7 = 33,429

And

Ordering cost per order = $57 per order

Annual holding cost per unit per year is 20% of $5.25 per kg which is $1.05.

So by putting values, we have:

Economic Order Quantity = Square Root (2 * 33,429 * 57 / 1.05)

Economic Order Quantity = 1905 kgs