Question

Now consider the case in which the manufacturer offers a marginal unit quantity discount for the plywood. The first 20,000 square feet of any order are sold at $1 per square foot, the next 20,000 square feet are sold at $0.98 per square foot, and any quantity larger than 40,000 square feet is sold for $0.96 per square foot. What is the optimal lot size for Prefab given this pricing structure? How much cycle inven

Answer 1

Answer:

Explanation:

We can use the following method to solve the given problem

We are given following

Annual demand,

D = 20000*12

D = 240,000 sqft

Fixed order cost, is given as

S = $ 400

Considering the unit cost, is given as

C = $ 1

Holding cost, H = 1*20% = $ 0.2

EOQ = sqrt(2DS/H)

= √(2*240000*400/0.2)

= 30,984 sq ft

This is higher than 20,000 and less than 40,000 sq ft. For this reason, the applicable price for this quantity is $ 0.98

For C = $ 0.98, holding cost, H = 0.98*20% = $ 0.196

Revised EOQ = sqrt(2*240000*400/0.196) = 31,298 sq ft

Total annual cost of EOQ policy = D*C + H*Q/2 + S*D/Q

= 240000*0.98 + 0.196*31298/2 + 400*240000/31298

= $ 241,334.5

Now consider the next level of price, C = $ 0.96

Holding cost, H = 0.96*20% = $ 0.192

EOQ = sqrt(2*240000*400/0.192)

= 31633 sqft

This amount is will not be feasible for this price, because it requires a minimum order of 40000 sqft.

Therefore, Q = 40,000

Total annual cost = 240000*0.96 + 0.192*40000/2 + 400*240000/40000

Total annual cost = $ 236,640

Total annual cost is lowest for order quantity of 40,000 sq ft.

1) Optimal lot size = 40,000 sq ft.

2) the annual cost of this policy

= $ 236,640

3) the cycle inventory of plywood at Prefab = Q/2 = 40000/2

At prefeb= 20,000 sq ft

4) let's assume the manufacturer sells all plywood at $ 0.96, then

Holding cost, H = 0.96*20%

H= $ 0.192

EOQ = sqrt(2*240000*400/0.192)

EOQ = 31633 sqft

Total annual cost = 240000*0.96 + 0.192*31633/2 + 400*240000/31633

Total annual cost = $ 236,471.6

Difference in total annual cost = 236640 - 236471.6 = $ 168.4