Linear regression

  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