I NEED HELP WITH QUESTION 15 For a certain drug the rate of

I NEED HELP WITH QUESTION #15

For a certain drug, the rate of reaction in appropriate units is given by R\'(t) = 5/t+7/t^2, where is measured in hours after the drug is administered. Find the total reaction to the drug from t = 1 to t = 7. Round to two decimal places, if necessary. Find the producers surplus if the supply function of some item is given by S(q) = q^2 + 2q + 8.Assume supply and demand are in equilibrium at q = 30. P(x) = -x^3 + 12x^2 - 36x + 400, x greaterthanorequalto 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. A company determines that its marginal revenue (in dollars per day) is given by MR(t) - 140e^t. The company\'s marginal cost (in dollars per day) is given by MC(t) = 60 - 0.4t. Find the total profit from t = 0 to t = 9 (the first 9 days). A company knows that unit cost C and unit revenue R from the production and sale of x units are related by C = R^2/188,000+4001. Find the rate of change of revenue per unit when the cost per unit is changing by $8 and the revenue is $2000. After a new firm starts in business, it finds that its rate of profit (in hundreds of dollars) after t years 15) of operation is given by P\'(t) = 3t^2 + 10t + 11. Find the profit in year 3 of the operation. The revenue generated by the sale of x bicycles is given by R(x) = 30.00x - x^2/200. Find the marginal revenue when x = 500 units. Suppose the supply function of a certain item is given by S(q) = 2q + 7, and the demand function is given by D(q) = 27 - q^2/3 Find the producers\' surplus. If the price of a product is given by P(x)=1024/x+1200, where x represents the demand for the product, find the rate of change of price when the demand is 2.

Solution

You\'re going to take the definite integral of P\'(t) from 5 to 6 to add up all rates of profit into a whole

(3t^2+10t+11)dt = t^3+5t^2+11t evaluated at 3 and 3

(3^3+5*3^2+11*3)-(2^3+5*2^2+11*2)= 105 -50 = 55

They make $5500 in the 3 year of the business.