A hospital needs 2,900 units of a medicine throughout the year. The purchasing cost varies with the size of the order. If the number of units of the medicine that the hospital orders is below 100, the supplier charges $30 per unit; if it is between 100 and 499, the price is $27 each; and if they order 500 units and above, it is $26 per unit. The holding cost per unit per year is $30, as the medicine must be kept in a special device to prevent spoilage. The ordering cost is $10. Required:
a. How many units of medicine should the hospital order to minimize their total annual cost?
b. What is the minimum annual total cost?

a. 100 units are ordered  

b. Minimum Total annual cost = 80090

Explanation:

Given that,

D=2900.

C = $30 IF q<100

    = $27 IF 100<Q<499.

    = $26 IF Q>500.

C(H) = $30

C(O) = $10.

EOQ = √(2*D*C(O)/C(H))

        = √( 2*2900*10/30)

        = √( 1933.3333)

         = 43.97

TAC if 44 units are ordered =  (2*D*C(O)*C(H))+D*C

                                             = 2*2900*10*30+ 2900*30

                                             = 1319.09+ 87000 = 88319.09

TAC if 100 units are ordered  = 2900/100*10+ 100/2*30+ 2900*27

                                                = 29*10+ 50*30+2900*27

                                                = 290+1500+78300

                                                = 1790 + 78300 = 80090

if 500 units are ordered  = 2900/500*10+ 500/2*30+2900*26

                                        = 58+ 7500+75400= 82958.

∴ we get

100 units are ordered  

Minimum Total annual cost = 80090.

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