Final answer:
To determine whether to take advantage of the price break, we compare the costs of the two offers. With the price break, the total cost is less than without the price break, making it more economical to take advantage of the price break.
Step-by-step explanation:
In order to determine whether to take advantage of the price break for purchase quantities of 2,000 or greater, we need to compare the costs of the two offers. Currently, the ordering cost is $250 per order. Let's calculate the number of orders needed to meet the demand of 25,750 units annually:
Total demand / units per order = 25,750 / 2,000 = 12.875 orders
Rounding up to the nearest whole number, we can estimate that 13 orders will be placed. The total ordering cost then becomes: 13 * $250 = $3,250
Now let's calculate the holding cost. We know that the item cost is $10 and the holding cost is 33% of the item cost, so the holding cost per unit is: $10 * 33% = $3.30
The total holding cost is then: $3.30 * 25,750 = $84,975
Adding the ordering cost and the holding cost, the total cost without the price break is: $3,250 + $84,975 = $88,225
With the price break of $50 per order, the total ordering cost becomes: (13-1) * $250 - $50 = $2,950
The total cost with the price break is then: $2,950 + $84,975 = $87,925
The total cost with the price break is less than the total cost without the price break, therefore it is more economical to take advantage of the price break for purchase quantities of 2,000 or greater.