Chapter C, Problem 1P

Bold Vision, Inc., makes laser printer and photocopier toner cartridges. The demand rate is 625 EP cartridges per week. The production rate is 1,736 EP cartridges per week, and the setup cost is $100. The value of inventory is $130 per unit, arid the holding cost is 20 percent of the inventory value. Bold Vision operates 52 weeks a year. What is the economic production lot size?

Summary Introduction

Interpretation: The Economic production of the lot of printer and cartridges made by the company are to be calculated.

Concept Introduction: Economic production of a lot is the quantity produced at lowest stock value. It is the minimum of total cost that requires for output.

Answer to Problem 1P

Economic production of the lot is 625.

Explanation of Solution

Given information:

Demand rate per week = 625 units, Production Rate per week = 1,736 Units and Holding cost = 20% of Stock value

Economic Order Quantity is the ideal quantity of stock to order for a given product.

  $EconomicOrderQuantity=\sqrt{\frac{2\times Demand\times Ordering\mathrm{Cos}t}{Carrying\mathrm{Cos}t}}$

  $Q=\sqrt{\frac{2DS}{H}}$

The demand rate per week = 625 units

This means $Demandrateper\text{ day}\text{=}\frac{625}{7}=89.28Units$

Production Rate per week = 1,736 Units

  $ProductionRateperDay=\frac{1,736}{7}=248Units$

Holding cost = 20% of Stock value

  $=0.20\times \$130=\$26$

The Economic Production of Lot size,

  $\begin{array}{l}ELS=\sqrt{\frac{2DS}{H}\sqrt{\frac{p}{p-d}}}\\ =\sqrt{\frac{2\times 625\times 52\times \$100}{\$26}}\sqrt{\frac{248}{248-89.28}}\\ =625Units\end{array}$

So, 625 units are required for the economic production lot size.