Question

A plastic moulding firm produces and uses 24000 Teflon bearing inserts annually. The cost of setting up for production is Rs 700, and the weekly production rate is 1000 units. If the production cost is Rs. 55 per unit and the annual carrying cost is 15 per unit, how many units should the firm produce during each production run ?

• A. 1066
• B. 2040
• C. 1443
• D. 4080

Answer 1

The correct option is B 2040

The demand and production rates must be in the same units. So we arbitrarily put both into annual terms,

$\text{Assuming 52 - weeks/ year.}$

$\text{Economic production Quantity}$

$\left(Q\right)=\sqrt{\frac{2D{C}_o}{C_c}\left(\frac{k}{k-d}\right)}$

$\text{Where}$

$C_o\text{= Cost of ordering/setting up}$

$C_c\text{= Annual carrying cost}$

$\text{D = Annual demand}$

$\text{k = Production rate =}1000\times 52\text{weeks =}52000$

$\text{d = Consumption rate = 24000}$

$\therefore Q=\sqrt{\frac{2D{C}_o}{C_c}}\sqrt{\frac{k}{k-d}}=\sqrt{\frac{2\times 24000\times 700}{15}}\times \sqrt{\frac{52000}{52000-24000}}$

$\text{= 2040 units}$