Please show work

3. Jane owns a candy store in a local mall. Each December, Jane only sells holiday samplers. With the help of some business majors on coop from Northeastern, Jane has found the following model for her profit function: P(x) = (24.8x 0.2x2)e "0 where P(x)is the profit in dollars if each sampler is sold for x dollars. Carefully enter the function P(x) into , on your calculator. Check that you have entered the function correctly by computing P(5). You should obtain 92.67729319. (a) (6 points) From the past sales experience, Jane knows that the sale price of each sampler should not be more than $30 but she doesn't want to sell sampler for less than $4. Use a derivative and your calculator to determine the price that maximizes profit. Write the answer with all the decimal places the calculator gives. Calculator answer (with units) : (b) (6 points) Show in two different ways that the price you found in part (a) maximizes the profit. () (2 points) What is the maximum profit? Round to 2 decimal places and give your answer with unit