) A company determines that its marginal revenue per day is given by R'(t) = 100et , R(0) = 0, where R(t) = the revenue, in dollars, on the tth day. The company's marginal cost per day is given by C'(t) = 140 - 0.3t, C(0) = 0, where C(t) = the cost, in dollars, on the tth day. Find the total profit from t = 0 to t = 5 (the first 5 days). Round to the nearest dollar. Note: P(T) = R(T) - C(T) = T 0 ∫ [R'(t) - C'(t)] dt.

Lin corporation has a single product whose selling price is $136 per unit and whose variable expense is $68 per unit. the company’s monthly fixed expense is $32,400. required: 1. calculate the unit sales needed to attain a target profit of $5,000. (do not round intermediate calculations.) 2. calculate the dollar sales needed to attain a target profit of $8,400.

(30 total points) suppose a firm’s production function is given by q = l1/2*k1/2. the marginal product of labor and the marginal product of capital are given by: mpl = 1/ 2 1/ 2 2l k , and mpk = 1/ 2 1/ 2 2k l . a) (12 points) if the price of labor is w = 48, and the price of capital is r = 12, how much labor and capital should the firm hire in order to minimize the cost of production if the firm wants to produce output q = 18?

Suppose life expectancy in years (l) is a function of two inputs, health expenditures (h) and nutrition expenditures (n) in hundreds of dollars per year. the production function is upper l equals ch superscript 0.40 baseline upper n superscript 0.60l=ch0.40n0.60. beginning with c = 1, a health input of $400400 per year (hequals=44) and a nutrition input of $400400 per year (nequals=44), show that the marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing. the marginal product of health expenditures when h goes from 44 to 55 is nothing, and the marginal product of health when h goes from 66 to 77 is nothing. (round your answers to three decimal places.)