Question

A gift shop sells little lentils—cuddly animal dolls stuffed with dried lentils—at a very steady pace of 10 per day, 310 days per year. the wholesale cost of the dolls is $5, and the gift shop uses an annual interest rate of 20 percent to compute holding costs. (a) if the shop wants to place an average of 20 replenishment orders per year, what order quantity should it use? (b) if the shop orders dolls in quantities of 100, what is the implied fixed order cost? (c) if the shop estimates the cost of placing a purchase order to be $10, what is the optimal order quantity?

Answer 1

Sales = 10 dolls/days

Annual sales = D = 10 dolls/days × 310 days

D = 3100 dolls / year

Wholesale cost = $5/doll

Holding cost = h = $5 * 20% = $1 / doll

A = Fixed cost

A) 3100 / 20 = 155 dolls / order

B) Optimal Order Quantity = 100 =
`√(2AD/h)`

100 =
`√((2*3100*A)/1)`

A = $ 1.612

The implied fixed cost per doll is $ 1.612

C) Optimal Order Quantity =
`√(2AD/h)` =
`√((2*3100*10)/1)` = 249 Dolls

The optimal order quantity is 249 dolls

Answer 2

Frequency of filling dolls = 10 / day

D/Q = 310 / year

Production cost c = $5.00

Therefore, the demand = 301 * 10 = 3,100 dolls

The Annual interest rate = 20%

Therefore, holding cost = 0.2 * 5 = $1 per year

a) F = 20, Q = D / F = 3,100 / 20 = 155

b) 100 = Q = SQRT[2AD/h] = SQRT[2a(3100)/1] = 78.74 SQRT[A]

Therefore, A = $1.61

c) Q = SQRT[2AD/h] = SQRT[2(10)(3100)/1] = 249