An electronics firm uses 600 cases of transistors each year. The cost of storing one case for a year is 90 cents, and the ordering fee is $30 per shipment. How many cases should the firm order each time to keep total cost at a minimum, assuming the transistors are used at a constant rate throughout the year and that each shipment arrives just as the preceding shipment has been used up?

Question

An electronics firm uses 600 cases of transistors each year. The cost of storing one case for a year is 90 cents, and the ordering fee is $30 per shipment. How many cases should the firm order each time to keep total cost at a minimum, assuming the transistors are used at a constant rate throughout the year and that each shipment arrives just as the preceding shipment has been used up?

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Total Cost = storage cost + ordering cost + purchase cost

Ordering cost = (Ordering cost per shipment)(# of cases in shipment)
OC = ($30)(600/x) = 18000/x

Purchasing Cost = (total of cases ordered)(cost per case)
PC = (600)(x)
PC = 600x

Storage Cost = (average # of cases stored)(storage cost per case)
SC = 18000/x(.90) = 16200/x

x would represent cost per case

TC = 16200/x + 18000/x + 600x
TC = 34200/x + 600x
TC = 34,200 + 600x^2

I am even getting close?

I agree on OC, and PC.

However, the cost of storing depends on how long the cases are there before used. One uses 600 cases/yr, so timestored= casesordered/(600case/yr). But these are not there the entire period, the average is 1/2 *x
Sc=1/2 x* x/600 *.90 check my thinking on this: units are
SC= cases*cases/(cases/yr)*dollars/case, so the units work out.

Now add all the costs, and to get min, take the derivative for cost with respect to x, set to zero, and solve for x.

How would you figure out dollars per case?

Answer 1

To figure out the cost per case, you need to gather information about the prices from the supplier or manufacturer. Typically, electronics firms negotiate the cost per case with their suppliers based on factors such as volume of orders, long-term partnerships, and market conditions.

Here are a few steps you can take to determine the cost per case:

1. Contact your supplier: Reach out to the supplier or manufacturer you plan to order the transistors from. Inquire about their pricing structure and any discounts available for bulk orders.

2. Request a quote: Provide the supplier with the quantity of cases you plan to order and ask for a detailed quote. This quote should include the unit price per case based on the specified order quantity.

3. Compare multiple suppliers: It's always a good idea to compare quotes from different suppliers to ensure you are getting the best possible price. Consider factors such as quality, lead time, and customer service along with the cost per case.

4. Negotiate if possible: If you have a good relationship with the supplier or if you plan to place regular and sizable orders, you may have some leverage to negotiate for a better price per case. Always be respectful and professional during negotiations.

By following these steps, you can determine the cost per case, which will then allow you to calculate the total cost and determine the optimal order quantity to minimize costs.