b) 16x^3 - 40x^2 = 25x
3. solve -4x^4 + 60x^3 = 200x^2 (5 marks)
4. determine the x- intercepts of the graph of each polynomial function.
a) 6x^3 + 13x^2 + 2x
b) -36x^4 + 14x^3 + 2x^2
5. The profit, P, of a video company (in thousands of dollars), is given by P(x) = -5x^2 + 550x - 5000, where x is the amount spent on advertising, in thousands of dollars.
a) Determine the amount spent on advertising that will result in a profit of 0$. In other words, you will determine the amount that must be spent on advertising in order for the company to break even. Describe the relationship between these values and the graph of P(x) (6 marks)
b) how much should be spent on advertising to achieve a maximum profit? (2 marks)
c) what is the maximum profit? (2 marks)
d) graph the function and state the domain (4 marks)
6. A music store sells an average of 160 CDs per week at 24$ each. The cost of purchasing x music CDs is C(x) = -0.003x^2 + 4.2x + 1000. A market survey indicates that for each 50 cent decrease in price, two additional CDs will be sold per week.
a) Determine the demand, or price, function (7 marks)
b) What is the price of each CD when 170 are sold weekly and when 200 are sold weekly? 3 marks)
c) Determine the revenue function (2 marks)
d) which of the following results in greater revenue: the sale of 170 CDs or the sale of 200 CDs? Justify your answer. (3 marks)
e) Determine the profit function (2 marks)
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