1. A company’s total cost, in millions of dollars, is given by 𝐶(𝑡) = 120 − 80𝑒
−𝑡 where t =
time in years. Find the marginal cost when t = 4.
2. 𝑃(𝑥) = −𝑥
3 + 12𝑥
2 − 36𝑥 + 400, 𝑥 ≥ 3 is an approximation to the total profit (in
thousands of dollars) from the sale of x hundred thousand tires. Find the number of hundred
thousands of tires that must be sold to maximize profit.
3. Given the revenue and cost functions 𝑅 = 28𝑥 − 0.3𝑥
2
and 𝐶 = 5𝑥 + 9, where 𝑥 is the daily
production, find the rate of change of profit with respect to time when 10 units are produced
and the rate of change of production is 4 units per day.
4. Find the producers’ surplus at a price level of 𝑝̅= $30 for the price-supply equation
𝑝 = 𝑆(𝑥) = 14 + 0.0004𝑥
2
