1. For the cost function (given in dollars), find the marginal cost of 1,521 units. {image}
$781.50
$21.50
$797.50
$802.50 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. For the given cost and demand functions, find the production level that will maximize profit. {image} . Find the answer correct to the whole number.
x = 21
x = 24
x = 13
x = 36 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. An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial cost of designing the airplane and setting up the factories in which to build it will be 300 million dollars. The additional cost of manufacturing each plane can be modeled by the function {image} where x is the number of aircraft produced and m is the manufacturing cost, in millions of dollars. The company estimates that if it charges a price p (in millions of dollars) for each plane, it will be able to sell x (p) = p. Find the cost function.
{image} 1. 2. 4. 3. 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 baseball team plays in a stadium that holds 55,000 spectators
A baseball team plays in a stadium that holds 55,000 spectators. With ticket prices at $9 the average attendance had been 28,000. When ticket prices were lowered to $8 the average attendance rose to 31,000. How should ticket prices be set to maximize revenue?
p = $9.17
p = $9.67
p = $18.33
p = $4.58 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. The manager of a 108-unit apartment complex knows from experience that all units will be occupied if the rent is $984 per month. A market survey suggests that, on the average, one additional unit will remain vacant for each $12 increase in rent. What rent should the manager charge to maximize revenue?
$1,275
$95
$2,280
$1,140 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