And because price cannot be negative we know that but

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Unformatted text preview: , we know that . But in order to keep , we must have . Therefore, the domain is . (B) Find the Revenue function . (It should be a function of just the variable , no .) Solution: . (C) If the goal is to maximize the daily Revenue, how many hats should be made each day, and what should be the selling price (in dollars) for each hat? Show all details clearly. Solution: is a continuous function defined on a closed interval . So the closed interval method can be used to find the absolute max. We need to find the critical values of the function by finding and then setting and solving for x. The derivative is . When we set and solve for x, we find the critical value . Finally, we make a list of the important x-values and find their corresponding values. important x values (endpoint) (critical) (endpoint) We see that the maximum Revenue occurs when hats are made each day. The corresponding selling price will be dollars per hat. (D) Find the Profit function Solution: . (It should be a function of the variable .) . (E) If the goal is to maximize the daily Profit, how many hats should be made each day, and what should be the selling price (in dollars) for each hat? Solution: We use the closed interval method again. We find the critical values of the function by setting and solving for x. The derivative is . When we set and solve for x, we find the critical value . Finally, we make a list of the important x-values and find their corresponding values. important x values (endpoint) (The company is losing $7 per day!!) (critical) (endpoint) (losing money) We see that the maximum Profit occurs when hats are made each day. The corresponding selling price will be dollars per hat....
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This document was uploaded on 02/17/2014 for the course MATH 1350 at Ohio University- Athens.

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