The annual inventory cost C for a manufacturer is given below, where Q is the order size when the inventory is replenished. Find the change in annual cost when Q is increased from 347 to 348, and compare this with the instantaneous rate of change when Q = 347. (Round your answers to two decimal places.) C = 1,017,000/ Q + 6.8QChange in C= C(360)=

Change in annual cost is 1.63 (decreasing).

Instantaneous rate of change is 1.65 (decreasing).

Step-by-step explanation:

Given that,

The annual change in cost is given by,  

Calculate the value of cost at Q = 347 and Q =348 by substituting the value in cost function.

Calculating value of C at Q=347,

Calculating value of C at Q=348,

Substituting the value,  

Negative sign indicate that there is decrease in annual cost when Q is increased from 347 to 348

Therefore, change is annual cost is 1.63  (decreasing).

Instantaneous rate of change is given by the formula,  

Rewriting,

Now calculate \dfrac{C\left(Q+h\right) by substituting the value Q+h in cost function,

Therefore,  

By using distributive law,

Cancelling out common factors,  

Now, LCD of and is . So multiplying first term by  and second term by

Therefore,  

Simplifying,  

Factoring out h from numerator,  

Cancelling out h,  

Calculating the limit by plugging value h = 0,

Given that Q=347,

Negative sign indicate that there is decrease in instantaneous rate when Q is 347

Therefore, instantaneous rate of change at Q=347 is 1.65  (decreasing).