When a company spends x (note that x must be non-negative) thousand dollars on marketing its product on internet, f(x) units of this product will be sold where When this company spends another y thousand dollars on marketing its product on TV, an additional g(y) units of this product will be sold where Hence, when the company spends x thousand dollars to market its product on internet and y thousand dollars to market its product on TV, total sales is given by f(x)+g(y). a. [21 Points] Suppose the company has a total of $10000 dollars and all of it must be spent on marketing the product on internet and TV. How much of these $10000 dollars should be allocated on marketing the product on internet so that the total sales is maximized (i.e., so that the units sold in total will be highest). Verify that the number you found maximizes the sales by using the first derivative test (Hint: When you are spending x on internet advertising, you have y=10-x to spend on TV advertising ). b. [14 Points] How much of these $10000 dollars should be allocated on marketing the product on internet so that the rate of change of the total sales is maximized. Verify that the number you found maximizes the rate of change of the total sales by using the second derivative test.