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I have a website where I offer cash rebates for buying stuff. For instance, if someone purchases a pair of shoes, I give them a $10 cash rebate. For that particular sale I will receive a commission of say, $25, so my net revenue from that offer is $15. The goal is to offer a rebate that is large enough that lots of people are incentivized to purchase the pair of shoes, but not so large that I will be giving most of my commissions away in the form of cash rebates. I have tested the number of shoes sold at 2 different cash rebates so I have two sets of coordinates for the demand function where x is the payout and y is the number of shoes sold.They are (5,15) and (10,40). We can assume that the slope is linear.I want to find the size of the cash rebate that maximizes total profits.How would I do this?
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