Profit Function


Annual profit in thousands of dollars is given by the function, P(x) = 100√(x  – 5) + 3,000, where x is the number of items sold in thousands, x ≥ 5.

1.describe the meaning of the number 5 in the formula, in terms of its meaning in relation to the profit.

2.describe the meaning of the number 3000 in the formula, in terms of its meaning in relation to the profit.

3.find the profit for 5 different values of x

4.graph the profit function over its given domain; use the 5 values calculated in part 3 to construct the graph and connect these points with a smooth curve in Excel or another graphing utility. Insert the graph in a Word file and attach the graph in a Word file to the class DB thread.

5.will this profit function have a maximum, if so, what is it?

6.what steps should the company take to prepare for your answer to part 5?


Andrew sets out to cycle from Kirkton to Simsburgh at exactly the same time as Mike left Simsburgh to cycle to Kirkton along the same route. The two passed each other at the point on the route 4 miles from Kirkton. Each cyclist continued to his destination turned and immediately started cycling back towards his starting point at the same rate. This time they met 2 miles from Simsburgh. Assuming that Andrew and Mike travelled at constant speeds, how far is it from Kirkton to Simsburgh? Given that Andrew’s speed is v mph what is Mike’s speed?

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