Question

Question 9 Assume: Demand 3000 units/year Inventory value $80/unit Order placement cost $400/order Annual carrying costs $0.30 per dollar held/yr or"3096" If you supplier calls with a special IX discount of 5%, how much should you buy? Buy a Quantity of 1,334 Buy a Quantity of 1,565 Buy a Quantity of 859 Buy a Quantity of 1462 Buy a Quantity of 1,608 Answers:

Answer 1

Q 9.

Demand, D = 3000 units/year

Inventory value, C = $ 80 / unit

Order placement cost, S = $ 400 per order

Annual carrying rate, i = 30%

Holding cost, H = 80*30% = $ 24

B15 2 Annual demand, D- 3 Order/setup cost, S- 4 Unit cost, C 5 Holding cost, H 6 1x discount, x= 7 8 Total Cost, TC (1-x)HQA2/2D+S+(1-x)QC+(D-Q)(C+SORT(2SH/D)) 9 For minimizing cost, d(TC)/dQ 0 10 d(TC)/dQ=d(1-x)HON2/2D+5+(1-x)QC+(D-Q)(C+SQRT(25H/D)))/dQ=0 11 2(1-x)HO/2D-(xC+SORT(2SH/D)) 0 12 2(1-x)HO/2D-xC+SORT(2SH/D) 13 Q-2D(xC+SORT (2SH/D))/(1-x)H) 14 15 Order quantity for 1X discount, Q 16 17 18 Total annual cost, TC= 19 20 21 3000 400 80 24 5% 1 time discount 859 245,184

Excel formula for Q =2*B2*(B6*B4+SQRT(2*B3*B5/B2))/(2*(1-B6)*B5)

for Total annual cost =(1-B6)*B5*B15^2/(2*B2)+B3+(1-B6)*B15*B4+(B2-B15)*(B4+SQRT(2*B3*B5/B2))

ANSWER: 859