Whole Nature Foods sells a gluten-free product for which the annual demand is 5,000 boxes. At the moment, it is paying $6.40 for each box; carrying cost is 25% of the unit cost; ordering costs are $25. A new supplier has offered to sell the same item for $6.00 if Whole Nature Foods buys at least

Question

Whole Nature Foods sells a gluten-free product for which the annual demand is 5,000 boxes. At the moment, it is paying $6.40 for each box; carrying cost is 25% of the unit cost; ordering costs are $25. A new supplier has offered to sell the same item for $6.00 if Whole Nature Foods buys at least 3,000 boxes per order. Should the firm stick with the old supplier, or take advantage of the new quantity discount?

Accepted Answer

Step 1, under the lowest possible price of $6.00 per box:
Economic order quantity, using Equation (12-10):

[latex]Q^* = \sqrt{\frac{2DS}{IP}}[/latex] (12-10)

[latex]Q^*_{\$ 6.00} = \sqrt{\frac{2(5,000)(25)}{(0.25)(6.00)}} = 408.25[/latex], or 408 boxes

Because 408 < 3,000, this EOQ is infeasible for the $6.00 price. So now we calculate [latex]Q^*[/latex] for the next-higher price of $6.40, which equals 395 boxes (and is feasible). Thus, the best possible order quantities are 395 (the first feasible EOQ) and 3,000 (the price-break quantity for the lower price of $6.00).

Step 2 uses Equation (12-9) to compute the total cost for both of the possible best order quantities:

[latex]TC = \frac{D}{Q} S + \frac{Q}{2}IP + PD[/latex] (12-9)

[latex]TC_{395} = \frac{5,000}{395}(\$25) + \frac{395}{2}(0.25)(\$6.40) + \$6.40(5,000) = \$316 + \$316 + \$32,000 = \$32,632[/latex]

And under the quantity discount price of $6.00 per box:

[latex]TC_{3,000} = \frac{5,000}{3,000}(\$25) + \frac{3,000}{2}(0.25)(\$6.00) + \$6.00(5,000) = \$42 + \$2,250 + \$30,000 = \$32,292[/latex]

Therefore, the new supplier with which Whole Nature Foods would incur a total cost of $32,292 is preferable, but not by a large amount. If buying 3,000 boxes at a time raises problems of storage or freshness, the company may very well wish to stay with the current supplier.

Question 12.SP.5: Whole Nature Foods sells a gluten-free product for which the...

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