Question

1. A certain firm posted an ad for a sales representative position paying $36,000 base salary plus commission. Based on his past experience, a salesman estimates he can generate $600,000 in sales annually.

1. What commission rate (as a percent of sales) must he earn to make $63,000 per year?

b.     Write an equation for his annual income as a function of his annual sales dollar volume.

c.     If the salesman wants to make $75,000 per year, by how much must he increase his annual sales volume (over the $600,000)?

d.     If the salesman wants to make $75,000 per year without increasing his sales volume, what commission rate must he receive?

2. The total cost C of producing x units of some commodity is a linear function. Records show that on one occasion, 100 units were made at a total cost of $200, and on another occasion, 150 units were made at a total cost of $275. Express the linear equation for total cost C in terms of the number of units x produced.

3. For most assets such as cars, stereo equipment, and furniture, the value decreases, or depreciates, each year. If the value of an asset is assumed to decrease by a fixed percentage of the original value each year, it is referred to as straight line depreciation.

a.     Suppose the value of a car which initially costs $20,000 depreciates by 10% of its original value each year. Find a formula for its value P(t) after t years.

b.     If a $500 washing machine is completely depreciated after 10 years (straight line depreciation), find a formula for its value W(t) after t years.

Answer 1