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Question
A store csn sell 500 pens, which cost the store 35 cents each, for $1 each. For each penny the store lowers the price, it can sell 20 more pens. For what price should the pens be sold for maximum profit?
I tried to use this equation- r(x) = (500+20x)(1-0.01x) and set its dervative to 0 to solve for x. however I did not get the right answer. I will appreciate your help in this question. Thanks
What to note is that since theyare sold for $1 and cost 35c, the profit is 65c each.
The equation you have then becomes r(x) = (500+20x)(0.65-0.01x).
I dealt with cents and used the equation r(x) = (500+20x)(65-x).
Taking the derivative as stands is using the product rule,
so r'(x) = (500+20x)(-1) + 20(65-x). To optimize, set r'(x) = 0 and solve for x.
Working this out should give you the pens will generate 45c profit each.
That means the pens sold will be over 2000, but redo it with the equation given
to find the answer.
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