022 Exam 1 Sample A, Problem 5
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Find the marginal revenue and marginal profit at , given the demand function
and the cost function
Should the firm produce one more item under these conditions? Justify your answer.
Foundations: 

Recall that the demand function, , relates the price per unit to the number of units sold, .
Moreover, we have several important important functions: 

In particular, we have the relations 

and 

Finally, marginal profit at units is defined to be the effective cost of the next unit produced, and is precisely . Similarly, marginal revenue or cost would be or , respectively. 
Solution:
Step 1: 

Write the Basic Equation: 
!Final Answer:  With units, we have that the ladder is sliding down the wall at feet per second. }