Business Calc: sells 2000 units/month at $10 each; 250 more per $0.25/unit reduction

Gabenorris

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Help please (at least with setting up the equation)

A business sells 2000 units of a product per month at a price of $10 each. It can sell 250 more items per month for each $0.25 reduction in price. What price per unit will maximize monthly revenue?
 
Help please (at least with setting up the equation)

A business sells 2000 units of a product per month at a price of $10 each. It can sell 250 more items per month for each $0.25 reduction in price. What price per unit will maximize monthly revenue?
What are your thoughts?

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"Revenue" is "number of items sold" times "price". Suppose the price in dollars is p. That is 10- p less than $10 and so 4(10- p)= 40- 4p "reductions" of $0.25. Since you could sell 2000 units at $10 and you "can sell 250 more items per month for each $0.25 reduction in price", you sell 250(40- 4p) more than 2000 units. So how many items can you sell at price p? Multiply that by p to get the revenue. That will be a quadratic function- its graph is a parabola with vertex at the top. Find the vertex, and the maximum revenue, by completing the square.
 
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