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 − 0.3𝑥2 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 �̅� = $30 for the price-supply equation 𝑝 = 𝑆(𝑥) = 14 + 0.0004𝑥 2

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