Need help with this word problem: A store has been selling a line of cameras for

Question

Need help with this word problem:
A store has been selling a line of cameras for $50 each and hasbeen averaging sales of 8000 cameras a month. They decide toincrease the price but their market research indicates that foreach $1 increase in price, sales will fall by 100. Find the pricethat will maximize their revenue. Thank you. Need help with this word problem:
A store has been selling a line of cameras for $50 each and hasbeen averaging sales of 8000 cameras a month. They decide toincrease the price but their market research indicates that foreach $1 increase in price, sales will fall by 100. Find the pricethat will maximize their revenue. Thank you.

Explanation / Answer

Revenue function: R(x)=(8000-100x)*(50+x)                 =400000 +8000x -5000x -100x2                 =-100x2 +3000x +400000 differentiate the function and equate to zero. -200x+3000=0     x=3000/200       =15 best price =50+15 =65$

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