MATH 1325 QUIZ/PROJECT
Instruction: Please write your answers with all detailed calculations for each question on
separate sheets of paper then scan (or take picture) and submit to eCampus under the
same folder (Do not send them to my email).
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
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 Calculus homework help