Answer to Question #270263 in Calculus for mimi

Question #270263

A manufacturer knows that if x goods are demanded on a particular week, the total cost and revenue functions will be:𝐶(𝑥) = 14 + 3𝑥 𝑎𝑛𝑑 𝑅(𝑥) = 18𝑥 − 2𝑥 2 respectively.

i. Calculate the level of demand that will maximize profits (6 marks)

ii. Calculate the amount of profit that will be realized at this maximum point. (4 marks) 


1
Expert's answer
2021-11-24T02:33:39-0500

i)

profit function:

"P(x)=\ud835\udc45(\ud835\udc65)-\ud835\udc36(\ud835\udc65)=18x-2x^2-14-3x=-2x^2+15x-14"

"P'(x)=-4x+15=0"

level of demand that will maximize profits:

"x=15\/4=3.75"


ii)

amount of profit that will be realized at this maximum point:

"P_{max}(x)=-2\\cdot3.75^2+15\\cdot3.75-14=14.125"


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