13.26. county hospital orders syringes from a hospital supply firm. the hospital expects to use 40,000 per year. the cost to order and have the syringes delivered is $800. the annual carrying cost is $1.90 per syringe because of security and theft. the hospital supply firm offers the following quantity discount pricing schedule. 0–9,999 $3.40 20,000–29,999 3.00 40,000–49,999 2.60 determine the order size for the hospital

The order size=20,632 syringes

Explanation:

Step 1

Determine the expected total cost of the syringe;

Total cost=40,000

Step 2

Determine associated costs as follows;

Total associated costs=ordering cost+(carrying cost×number of syringes)

Total associated costs=800+(1.9×n)

Total costs=1.9 n+800

Step 3

Equating;

1.9 n+800=40,000

1.9 n=40,000-800

1.9 n=39,200

n=39,200/1.9

n=20,631.579=20,632 syringes

The order size=20,632 syringes

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