1) An electronics store sells an average of 60 entertainment systems per month at an average of Rs. 800 more than the cost price. For every Rs. 20 increase in the selling price, the store sells one fewer system. What amount over the cost price will maximize revenue?

2) Last year, a banquet hall charged Rs. 30 per person, and 60 people attended the hockey banquet dinner. This year, for every 10 extra people attending, the hall decreases the price by Rs. 1.50 per person. What group size would maximize the profit this year, and what would the maximum profit be?

3) The path of a rocket is given by the function: h(t) = −3t² + 30t + 73. a) What is the maximum height of the rocket? b) At what time does it reach that height?

4) A flare is fired vertically from the top of a platform. Its height (m) after t seconds is: h(t) = 4 + 30t − 5t². What is the maximum height that the flare reaches?

5) A swimming pool is treated periodically to control bacteria. The concentration t days after treatment is: C(t) = 30t² − 240t + 500. What is the lowest concentration of bacteria during the first week, and on which day?

6) Determine two numbers whose difference is 12 and whose product is a minimum.

7) Find two positive quantities whose sum is 18, if the sum of their squares is a minimum.

8) A magazine producer can sell 600 magazines at Rs. 6.00 each. For every Rs. 0.50 increase in price, 30 fewer magazines are sold. What price should she set to obtain the greatest revenue?

9) Find the vertex of the function A(w) = −4w² − 32w + 6. Is it a maximum or minimum?

10) Find the vertex of the function h(t) = 0.3t² − 1.2t + 4.5. Is it a maximum or minimum?

11) Find the vertex of the function F(g) = (1/3)g² + 4g − 6. Is it a maximum or minimum?

12) Find the vertex of the function d(t) = −3t² + 5t. Is it a maximum or minimum?