The change in annual cost when Q is increased from 340 to 341 is -1.23 and the instantaneous rate of change when Q = 340 is -1.25
<h3>How to find the Instantaneous rate of change?</h3>
The annual inventory cost C for a manufacturer is given as;
C = (1012000/Q) + 7.5Q
where Q is the order size when the inventory is replenished.
Now, the change in C can be calculated by evaluating the cost function at Q = 340 and Q = 341
Change in C = [1,012,000/341 + 7.5*341] - [1,012,000/340 + 7.5*340] ≈ -1.23
Instantaneous rate of change in C is first order derivative C':
C'(Q) = -1,012,000/(Q²) + 7.5
C'(340) = -1,012,000/(340²) + 7.5 ≈ -1.25
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