1. The marginal revenue from producing x units of a certain product is {image} (in dollars per unit). Find the increase in revenue if the production level is raised from 1,200 units to 1,600 units.
$16,725,333
$33,450,667
$43,485,861
$23,415,465
$30,105,597
$20,070,399 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. The supply function {image} for a commodity gives the relation between the selling price and the number of units that manufacturers will produce at that price. For a higher price, manufacturers will produce more units, so {image} is an increasing function of {image} . Let X be the amount of the commodity currently produced and let {image} be the current price. Some producers would be willing to make and sell the commodity for a lower selling price and are therefore receiving more than their minimal price. The excess is called the producer surplus. An argument similar to that for consumer surplus shows that the surplus is given by the integral  {image} . Calculate the producer surplus for the supply function {image} at the sales level {image} .
$12.00
$18.67
$8.00
$16.00
$9.33
$13.33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. A company modeled the demand curve for its product (in dollars) by {image} Use a graph to estimate the sales level when the selling price is $ Then find (approximately, using Simpson's Rule with n = 10) the consumer surplus for this sales level.
$24,720
$20,600
$22,660
$26,780
$10,300
$14,420 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. A hot, wet summer is causing a mosquito population explosion in a lake resort area. The number of mosquitos is increasing at an estimated rate of {image} per week (where t is measured in weeks). By how much does the mosquito population increase between the 5th and 9th weeks of summer?
20,848
11,226
22,452
16,037
12,830
17,641 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. Dye dilution is a method of measuring cardiac output
Dye dilution is a method of measuring cardiac output. If A mg of dye is used and c(t) is the concentration of the dye at time t, then the cardiac output over the time interval [0, T] is given by {image} Find the cardiac output over the time interval [0, 12] if the dye dilution method is used with 5 mg of dye and the dye concentration, in mg/L, is modeled by {image} , where t is measured in seconds.
0.125 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50