Question

Our home construction company consumes nails from our warehouse in 15-pound boxes. We use an average of 1414 boxes a year. The warehouse can provide nails at 42 boxes per day while our usage is 19 boxes per day. It costs $0.90 to place the typical order. Annual carrying costs are $0.65 per box. What will be our average number of boxes on hand if we order the EPQ boxes in each order

Answer 1

Answer:

23.155 units

Step-by-step explanation:

Economic Production Quantity (EPQ) helps to sustain the equilibrium between the ordering cost and carrying costs and it is given by the expression:

$EPQ=\sqrt{\frac{2DS}{H} }*\sqrt{\frac{P}{P-u} }$

where;

D = Annual demand

P = production rate

u = usage rate

S = setup cost

H = holding cost

Given that:

We use an average of 1414 boxes a year; D = 1414  boxes/year

The warehouse can provide nails at 42 boxes per day; P = 42 boxes/day

our usage is 19 boxes per day; u = 19 boxes/day

It costs $0.90 to place the typical order; S = $ 0.90/ order

Annual carrying costs are $0.65 per box; H = $0.65/ order

replacing our given parameters into the above formula; we have:

$EPQ=\sqrt{\frac{2*1414*0.90}{0.65} }*\sqrt{\frac{42}{42-19} }$

$EPQ= 62.57549287*1.351327849$

$EPQ= 84.56000618$

$EPQ=84.56 units$

Maximum average number of boxes $I_{max$ = $\frac{EPQ}{P}(P-u)$

$I_{max$ = $\frac{84.56}{42}(42-19)$

$I_{max$ = 46.31 units

average number of boxes on hand if we order the EPQ boxes in each order;

=  $\frac{I_{max}}{2}$

= $\frac{46.31}{2}$

= 23.155 units