Problem 1. The concentration C of a drug in the blood (in mg per liter) following its injection is a function of the dose a: (in mg) and the time t (in hours) since the injection: 0 = xte't (a) Find 0| (m,t)=(5,1)' What does this tell you about the concentration of drug in the blood stream? (b) Find a formula for the section Where a: = 5 and use it to nd m at (m,t)=(5,1) What are the units? What does this value tell you about the concentration of drug in the blood stream? (c) Find a formula for the section where t = 1 and use it to nd 80 593 (z,t)=(5,1) What are the units? What does this value tell you about the concentration of drug in the blood stream? Problem 2. The CobbDouglas function P = f(N, V) = 2N0'5V0'3 models the production of a small printing press P (in thousands of pages per day) as a function of the number of workers N and the value of the equipment V (measured in units of $25,000). (a) What is the production level of the company if it currently employs 100 workers and has 200 units (5 million dollars) worth of equipment? (b) Find a formula for the section P = f (N , 200) and use it to nd fN(100, 200). What are the units? What does this tell you about production at this company? (c) Find a formula for the section P = f (100, V) and use it to nd fV(100, 200). What are the units? What does this tell you about production at this company? Problem 3. The quantity Q = f(b, c) of beef that a community buys each week (in pounds) is a function of the price of beef 0 (in dollars per pound) and the price of chicken 0 (in dollars per pound). (a) Do you expect fb(b, c) to be positive or negative? Explain. (b) Do you expect fc(b, c) to be positive or negative? Explain. (0) Suppose f(b,c) = 70, 000, fb(10,4) = 4, 000, and 3200,29 = 2,000 Estimate f(1045,3.75)