Business: Exploring a Profit Maximization Problem Use a graphing calculator to further e...

Business: Exploring a Profit Maximization Problem Use a graphing calculator to further explore Example 2 (page 204) as follows:

a. Enter the price function y₁ = 400 - 10x and the quantity function y₂ – 20+2x into your graphing calculator.

b. Make y₃ the revenue function by defining y₃ = y₁y₂ (price times quantity).

c. Make y4 the cost function by defining y₄ = 200y₂ (unit cost times quantity).

d. Make y5 the profit function by defining y₅ = y₃ - y₄ (revenue minus cost).

e. Turn off y₁, y₂, y₃, and y₄ and graph the profit function y₅ on the window [0, 10] by [0, 10,000] and then use MAXIMUM to maximize it. Your answer should agree with that found in Example 2

Now change the problem!

f. What if the store finds that it can buy the bicycles from another wholesaler for $150 instead of $200? In y₄, change the 200 to 150. Then graph the profit y₅ (you may have to turn off y₄ again) and maximize it. Find the new price and quantity by evaluating y₁ and y₂ (using CALCULATE) at the new x-value.

g. What if cycling becomes more popular and the manager estimates that she can sell 30 instead of 20 bicycles per week at the original $400 price? Go back to y₂ and change 20 to 30 (keeping the change made earlier) and graph and find the price and quantity that maximize profit now.

Notice how flexible this setup is for changing any of the numbers.