Your business can sell 1,200 Sony 40-inch flat screen TVs per week if the price is set at $950, and 1,450 TVs if the price is $850 each. Assume that the demand function is a LINEAR function, that is, it can be written in f(x)=mx+b form. Using the above information... 1. The above information gives us two data points relating price to product demanded. What are the two data points? Write them as coordinates in the form (quantity demanded, price). 2. Find the demand function p(x). If needed, review how to find the equation of the line through two points 3. Draw a graph of the demand function with the number of units(x) on the horizontal axis and the price(p) on the vertical axis. Clearly mark the two data points from part a, and clearly show what the x and y-intercepts are. You can use software to make your graph (like desmos.com) or draw it on paper. Page of 2 Use the demand function to find the PRICE ELASTICITY OF DEMAND at each of the following prices and determine whether the TVs are ELASTIC or INELASTIC at that price. Note: If you search the internet for "price elasticity of demand" formula, there are several versions of this formula, some of which do not involve calculus at all. You need to use the version of the formula that is given in our textbook & lecture videos. 4. What is the Price Elasticity of Demand if the TVs are being sold at $6407 (round to the nearest hundredth as needed) Are the TVS ELASTIC or INELASTIC at this price? How did you determine? 5. What is the Price Elasticity of Demand if the TVs are being sold at $1000? (round to the nearest hundredth as needed) Are the TVs ELASTIC OF INELASTIC at this price? How did you determine? Now let's maximize our revenue! 6. First, use the demand function p(x) to find the revenue function. What is the revenue function for these TVs? 7. Use calculus to maximize the revenue function. (Must use calculus techniques to get credit) You must also show how you use calculus to confirm that this point is indeed a maximum. What number of units sold will maximize the weekly revenue? (Do not round, even though setting a fractional TV isn't possible. leave the answer unrounded so that all the math will work out neatly in the rest of the project. Your answer should have just one decimal place) 8. What is the maximum weekly revenue? (How much revenue will you make by selling the number of TVs you found in question 77) 9. What price will you need to sell each TV for in order to maximize your weekly revenue? 10. At that price, what is the price elasticity of demand
