A vendor can sell 400 souvenirs per day at a price of $2.00 each. Each increase of 30¢ in price decreases the number of sales by 50 per day. Souvenirs cost the vendor $1.20 each. What price should be charged to maximize profit?

I started with (400-50x)(2+.30x-1.20) I know that the max profit is 426 at 2.6 but is $2.60 my answer or do I add that to the $2.00? I am so confused. Please help if you can.

Eileen

Question

A vendor can sell 400 souvenirs per day at a price of $2.00 each. Each increase of 30¢ in price decreases the number of sales by 50 per day. Souvenirs cost the vendor $1.20 each. What price should be charged to maximize profit?

I started with (400-50x)(2+.30x-1.20)   I know that the max profit is 426 at 2.6 but is $2.60 my answer or do I add that to the $2.00?  I am so confused.  Please help if you can.

Eileen

anonymous · Answer

or it is actually max profit 426 at 2.6666 so is my answer $2.66?

anonymous · Answer

x is the number of 30 cent increases, so you would take the maximum of x, multiply it by 30 cents, and add it to your base $2 price:$$0.3(2.66)+2=$2.79$$

anonymous · Answer

Thank you so very very much!!!!