Lecture 4 Practice Question Answers

Note: In most of these problems, the key to finding some answers is to use other answers that you’ve already found. For instance, before you can find the value of MC, you may have to find TC first. Sometimes you can’t fill in the blanks in order they appear -- instead, you have to fill in later blanks, and then work backward. If you haven’t tried this approach, I encourage you to try again before looking at the answers below.

1.

L / q / APL / MPL
0 / 0 / --
5
1 / 5 / 5
6
2 / 11 / 5.5
5
3 / 16 / 5.33

To find the missing quantities, add the MPL values to previous quantities: 0 + 5 = 5, 5 + 6 = 11, and 11 + 5 = 16. (We can do this because ΔL = 1 every time.)

To find the APL values, divide q by L: 5/1 = 5, 11/2 = 5.5, and 16/3 = 5.33.

2.

L / q / APL / MPL
0 / 0 / --
3
5 / 15 / 3
6
10 / 45 / 4.5
7
15 / 80 / 5.333

To find the first missing L, solve the following: 3 = 15/L, so L = 15/3 = 5.

To find the first missing MPL value, use the formula: MPL = (15 - 0)/(5 - 0) = 3.

To find the next missing L, solve the following: 6 = (45 - 15)/(L - 5).

To find the missing APL, use the formula: APL = 45/10 = 4.5.

To find the last missing L, solve the following: 5.33 = 80/L, so L = 80/5.333) = 15.

To find the last missing MPL, use the formula: MPL = (80 - 45)/(15 - 10) = 7.

3.

q / TVC / TC / MC
0 / 0 / 20
10
1 / 10 / 30
15
2 / 25 / 45
20
3 / 45 / 65

To find the missing TVC values, add MC values to previous TVC values: 0 + 10 = 10, 10 + 15 = 30, 30 + 15 = 45. We know TFC = 20 because TC = 0 when q = 0, so just add 20 to each TVC to get the TC.

4.

L / q / APL / MPL
0 / 0 / --
10
5 / 50 / 10
20
10 / 150 / 15
25
15 / 275 / 18.33
20
20 / 375 / 18.75
10
25 / 425 / 17
5
30 / 450 / 15

Find the first missing APL using APL = q/L = 50/5 = 10.

Find the first missing q using APL = q/L: 15 = q/10, so q = 150.

Find the first missing MPL using MPL = q/L = (275 - 150)/(15 - 10) = 25.

Find the second missing APL using APL = q/L = 275/15 = 18.33.

Find the second missing q using MPL = q/L: 20 = (q - 275)/(20 - 15), so 100 = q - 275, so q = 375.

Find the third missing APL using APL = q/L = 375/20 = 18.75.

Find the third missing q using MPL = q/L: 5 = (q - 425)/(30 - 25), so 25 = q - 425, so q = 450.

5. Note: In this problem, your answers may differ slightly due to rounding or different methods of calculation (since some values can be calculated more than one way).

q / TFC / TVC / TC / ATC / MC
0 / 100 / 0 / 100 / --
0.8
50 / 100 / 40 / 140 / 2.8
0.4
150 / 100 / 80 / 180 / 1.2
0.32
275 / 100 / 120 / 220 / 0.8
.4
375 / 100 / 160 / 260 / 0.69
0.8
425 / 100 / 200 / 300 / 0.71
1.6
450 / 100 / 240 / 340 / 0.75

Find the first missing TVC using TVC = TC - TFC = 140 - 100 = 40.

Find the first missing ATC using ATC = TC/q = 140/50 = 2.8.

Find the first missing TC using ATC = TC/q: 0.8 = TC/275, so TC = 220.

Find the first missing q using MC = TC/q: 0.32 = (220 - 180)/(275 - q), so 0.32(275 - q) = 40, so 88 - 0.32q = 40, so 48 = 0.32q, so q = 150.

Find the second missing ATC using ATC = TC/q = 180/150 = 1.2.

Find the second missing TVC using TVC = TC - TFC = 220 - 100 = 120.

Find the second missing q using ATC = TC/q: 0.69 = 260/q, so q = 376.81. Actually, because ATC = 0.69 was a rounded figure, the actual TC = 375. I will use this number instead of 376.81 in the remaining calculations (but it’s okay if you used $376.81).

Find the second missing TC using ATC = TC/q: 0.71 = TC/425, so TC = 301.75. Again, because ATC = 0.71 was a rounded figure, the actual TC = 300.

Find the third missing TVC using TVC = TC - TFC = 300 - 100 = 200.

Find the last missing q using MC = TC/q: 1.6 = (340 - 300)/(q - 425), so 1.6(q - 425) = 40, so 1.6q - 680 = 40, so 1.6q = 720, so q = 450.

Find the last missing ATC using ATC = TC/q = 340/450 = 0.75.

Find the first missing MC using MC = TC/q = (180 - 140)/(150 - 50) = 0.4.

Find the second missing MC using MC = TC/q = (260 - 220)/(375 - 275) = 0.4.