# project #2 - Jerod Lane Calc Project#2 Due to the wonderful...

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Jerod Lane Calc Project #2 Due to the wonderful calculations we provided with OHaganbooks.com in their previous inquiry to maximize their business they have now asked us to help them out in another part of their business. This time around however we are asked to use calculus techniques to provide a better understanding inside the real business world with relative techniques that apply to they’re business specifically. We are first asked to determine the price that OHaganBooks should charge to obtain the largest weekly revenue and then use this to figure out what they’re largest revenue will be at that price. We are given the demand equation, q = - 2 p ^2 + 5 p + 6 (0 ≤ p ≤3.3) representing the copies sold. We want to find revenue and we know that revenue is equal to (price x quantity) having letter R represent Revenue, p representing price, and q representing quantity. R=p x q We can then substitute our known quantity and use the basic distribution method to achieve our new revenue equation. R=p ( - 2p ^2 + 5p + 6) R= -2p^3+5p^2+6p This new equation is going to be our starting point to find out the price at which largest weekly revenue is achieved. We are now going to take the derivative of this new equation. By doing this we are trying to maximize our revenue. R= -2p^3+5p^2+6p R = -6p^2+10p+6 From here we know that we have now achieved the equation that is going to help us find the highest possible price we should charge in order to maximize weekly revenue. Next we are going to set this new

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function equal to zero in order to find our two possible prices. It is not easily factorable so we are going to have to use the quadratic formula; our x in this will be our p representing price. =- ± - p b b2 4ac2a Our A value will be -6 Our B value will be 10 Our C value will be 6 After plugging in our value we get two answers: -\$0.46 and \$2.14. We know that it is not possible to charge a negative price so we know that the price we should charge in order to obtain the largest weekly revenue is \$2.14. Now that we have arrived at our price we should charge now all we have to do is plug this price into the
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project #2 - Jerod Lane Calc Project#2 Due to the wonderful...

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