Suppose that Caterpillar Inc., a leading manufacturer of construction and mining equipment, is trying to determine the size of a supply contract with an overseas bearing manufacturer for the year 2024. This is a specialized bearing that is used in few car models but also available in the spot market. The usage in 2024 is estimated as a normal random variable with mean 20,000 and standard deviation of 4,000 . Caterpillar has to determine how many it should purchase at \$20 each from overseas which will be binding regardless how many Caterpillar actually uses. If Caterpillar over-purchases (in other words overstock), it has to carry the extra stock for the entire year at the rate of \$5 per bearing. On the other hand, if Caterpillar under-purchases (under-stock), it has to purchase from the spot market to keep up with the usage. The price in the spot market is expected to be around \$26 per bearing. Caterpillar does not incur any additional costs from overstocking because those bearings left can later be used in 2024 . What is the size of the supply contract Caterpillar should sign to minimize its total purchasing and holding costs