Annual demand, D = 4000 units

Unit cost, c = $ 90

Order cost, S = $ 25

Carrying cost, H = 90*10% = $ 9

.

a)

Economic order quantity, Q = sqrt(2DS/H)

= sqrt(2*4000*25/9)

= 149

.

b)

Total annual cost = Purchasing + Ordering + Carrying

= D*c + S*D/Q + H*Q/2

= 4000*90 + 25*4000/149 + 9*149/2

= $ 361,342

.

c)

Number of orders per year = D/Q

= 4000/149

= 26.85

Optimal number of days between orders = 250 working days per year / Number of orders per year

= 250 / 26.85

= 9.31 days

.

d)

Daily demand, d = 16 units

Std dev, s = 4 units

Lead time, L = 5 days

For service level of 90%, z value = NORMSINV(0.9)

= 1.2816

Reorder point = d*L + z*s*sqrt(L)

= 16*5 + 1.2816*4*sqrt(5)

= 91.5

.

e)

Production cost, c = $ 80

Setup cost, S = $ 400

Production rate, p = 20 per day

Holding cost, H = 80*10% = $ 8

Economic production quantity, Q = sqrt(2DS/(H*(1-d/p)))

= sqrt(2*4000*400/(8*(1-16/20)))

= 1414 units

.

Annual total cost = D*c + S*D/Q + H*Q*(1-d/p)/2

= 4000*80 + 400*4000/1414 + 8*1414*(1-16/20)/2

= $ 322,263

.

We see that annual total cost of in-house production is lower

Therefore, the company should consider producing these popular valves in-house