10. A building materials company sells gravel. Suppose that C(x) = 0.5x² +3x %3D represents its estimated monthly cost, and R(x) =-0.002x + 5x - 10x represents its estimated monthly revenue, where x is in thousands of pounds of gravel sold. The profit is the difference between the revenue and the cost. NWhat is the profit function, P(x)?

0.9 The profit in dollars from the sale of x expensive watches is P(x)- 0.04x-2x+7x -5000. Find the marginal profit when (a) x=D100, (b) x- 2000, (c) x-5000 and (d) x- 10,000. (a) When x= 100, the marginal profit is $ (Round to the nearest integer as needed)

(b) Towns A and B are 12 km apart. A cyclist leaves A and travels to B at an average speed of y km/h. From B, he returns immediately to A with an average speed reduced by 2 km/h. (i) Find, in terms of y, the time taken for the journey from A to B. (ii) Find, in terms of y, the time taken for the return journey. (iii) Given that the total time spent to travel from A toB and back to A is 5 hours, write an equation satisfied by y. (iv) Solve the equation written in part (iii). (v) Give a simple reason why one of the values of y obtained in part (iv) is not valid.

The total profit in thousands of dollars, for a product is given by (see attachment) and x is the number of units produced. Determine the marginal profit function when x=15.