Determine the Optimal Q value for the following scenario. Market report: Demand
ID: 1166176 • Letter: D
Question
Determine the Optimal Q value for the following scenario.
Market report: Demand remains strong, and many fleets are still knocked out of the crabbing market. Expected market price remains $625 per 20lb container.
First Mate’s report: Well, finally some good news for a change. Seems like the storm made those little crabs extra fertile. We are pulling in crabs at record rates. The cost of finding the crabs is down from $5 per unit on average to $3.
Q FC VC TC MC P TR MR 0 12,500.00 - 12,500.00 - 625 0 1 12,500.00 105.00 12,605.00 105.00 625 625 625 2 12,500.00 220.00 12,720.00 115.00 625 1250 625 3 12,500.00 345.00 12,845.00 125.00 625 1875 625 4 12,500.00 480.00 12,980.00 135.00 625 2500 625 5 12,500.00 625.00 13,125.00 145.00 625 3125 625 6 12,500.00 780.00 13,280.00 155.00 625 3750 625 7 12,500.00 945.00 13,445.00 165.00 625 4375 625 8 12,500.00 1,120.00 13,620.00 175.00 625 5000 625 9 12,500.00 1,305.00 13,805.00 185.00 625 5625 625 10 12,500.00 1,500.00 14,000.00 195.00 625 6250 625 11 12,500.00 1,705.00 14,205.00 205.00 625 6875 625 12 12,500.00 1,920.00 14,420.00 215.00 625 7500 625 13 12,500.00 2,145.00 14,645.00 225.00 625 8125 625 14 12,500.00 2,380.00 14,880.00 235.00 625 8750 625 15 12,500.00 2,625.00 15,125.00 245.00 625 9375 625 16 12,500.00 2,880.00 15,380.00 255.00 625 10000 625 17 12,500.00 3,145.00 15,645.00 265.00 625 10625 625 18 12,500.00 3,420.00 15,920.00 275.00 625 11250 625 19 12,500.00 3,705.00 16,205.00 285.00 625 11875 625 20 12,500.00 4,000.00 16,500.00 295.00 625 12500 625 21 12,500.00 4,305.00 16,805.00 305.00 625 13125 625 22 12,500.00 4,620.00 17,120.00 315.00 625 13750 625 23 12,500.00 4,945.00 17,445.00 325.00 625 14375 625 24 12,500.00 5,280.00 17,780.00 335.00 625 15000 625 25 12,500.00 5,625.00 18,125.00 345.00 625 15625 625 26 12,500.00 5,980.00 18,480.00 355.00 625 16250 625 27 12,500.00 6,345.00 18,845.00 365.00 625 16875 625 28 12,500.00 6,720.00 19,220.00 375.00 625 17500 625 29 12,500.00 7,105.00 19,605.00 385.00 625 18125 625 30 12,500.00 7,500.00 20,000.00 395.00 625 18750 625 31 12,500.00 7,905.00 20,405.00 405.00 625 19375 625 32 12,500.00 8,320.00 20,820.00 415.00 625 20000 625 33 12,500.00 8,745.00 21,245.00 425.00 625 20625 625 34 12,500.00 9,180.00 21,680.00 435.00 625 21250 625 35 12,500.00 9,625.00 22,125.00 445.00 625 21875 625 36 12,500.00 10,080.00 22,580.00 455.00 625 22500 625 37 12,500.00 10,545.00 23,045.00 465.00 625 23125 625 38 12,500.00 11,020.00 23,520.00 475.00 625 23750 625 39 12,500.00 11,505.00 24,005.00 485.00 625 24375 625 40 12,500.00 12,000.00 24,500.00 495.00 625 25000 625 41 12,500.00 12,505.00 25,005.00 505.00 625 25625 625 42 12,500.00 13,020.00 25,520.00 515.00 625 26250 625 43 12,500.00 13,545.00 26,045.00 525.00 625 26875 625 44 12,500.00 14,080.00 26,580.00 535.00 625 27500 625 45 12,500.00 14,625.00 27,125.00 545.00 625 28125 625 46 12,500.00 15,180.00 27,680.00 555.00 625 28750 625 47 12,500.00 15,745.00 28,245.00 565.00 625 29375 625 48 12,500.00 16,320.00 28,820.00 575.00 625 30000 625 49 12,500.00 16,905.00 29,405.00 585.00 625 30625 625 50 12,500.00 17,500.00 30,000.00 595.00 625 31250 625 51 12,500.00 18,105.00 30,605.00 605.00 625 31875 625 52 12,500.00 18,720.00 31,220.00 615.00 625 32500 625 53 12,500.00 19,345.00 31,845.00 625.00 625 33125 625 54 12,500.00 19,980.00 32,480.00 635.00 625 33750 625 55 12,500.00 20,625.00 33,125.00 645.00 625 34375 625 56 12,500.00 21,280.00 33,780.00 655.00 625 35000 625 57 12,500.00 21,945.00 34,445.00 665.00 625 35625 625 58 12,500.00 22,620.00 35,120.00 675.00 625 36250 625 59 12,500.00 23,305.00 35,805.00 685.00 625 36875 625 60 12,500.00 24,000.00 36,500.00 695.00 625 37500 625 61 12,500.00 24,705.00 37,205.00 705.00 625 38125 625 62 12,500.00 25,420.00 37,920.00 715.00 625 38750 625 63 12,500.00 26,145.00 38,645.00 725.00 625 39375 625 64 12,500.00 26,880.00 39,380.00 735.00 625 40000 625 65 12,500.00 27,625.00 40,125.00 745.00 625 40625 625 66 12,500.00 28,380.00 40,880.00 755.00 625 41250 625 67 12,500.00 29,145.00 41,645.00 765.00 625 41875 625 68 12,500.00 29,920.00 42,420.00 775.00 625 42500 625 69 12,500.00 30,705.00 43,205.00 785.00 625 43125 625 70 12,500.00 31,500.00 44,000.00 795.00 625 43750 625 71 12,500.00 32,305.00 44,805.00 805.00 625 44375 625 72 12,500.00 33,120.00 45,620.00 815.00 625 45000 625 73 12,500.00 33,945.00 46,445.00 825.00 625 45625 625 74 12,500.00 34,780.00 47,280.00 835.00 625 46250 625 75 12,500.00 35,625.00 48,125.00 845.00 625 46875 625 76 12,500.00 36,480.00 48,980.00 855.00 625 47500 625 77 12,500.00 37,345.00 49,845.00 865.00 625 48125 625 78 12,500.00 38,220.00 50,720.00 875.00 625 48750 625 79 12,500.00 39,105.00 51,605.00 885.00 625 49375 625 80 12,500.00 40,000.00 52,500.00 895.00 625 50000 625 81 12,500.00 40,905.00 53,405.00 905.00 625 50625 625 82 12,500.00 41,820.00 54,320.00 915.00 625 51250 625 83 12,500.00 42,745.00 55,245.00 925.00 625 51875 625 84 12,500.00 43,680.00 56,180.00 935.00 625 52500 625 85 12,500.00 44,625.00 57,125.00 945.00 625 53125 625 86 12,500.00 45,580.00 58,080.00 955.00 625 53750 625 87 12,500.00 46,545.00 59,045.00 965.00 625 54375 625 88 12,500.00 47,520.00 60,020.00 975.00 625 55000 625 89 12,500.00 48,505.00 61,005.00 985.00 625 55625 625 90 12,500.00 49,500.00 62,000.00 995.00 625 56250 625 91 12,500.00 50,505.00 63,005.00 1,005.00 625 56875 625 92 12,500.00 51,520.00 64,020.00 1,015.00 625 57500 625 93 12,500.00 52,545.00 65,045.00 1,025.00 625 58125 625 94 12,500.00 53,580.00 66,080.00 1,035.00 625 58750 625 95 12,500.00 54,625.00 67,125.00 1,045.00 625 59375 625 96 12,500.00 55,680.00 68,180.00 1,055.00 625 60000 625 97 12,500.00 56,745.00 69,245.00 1,065.00 625 60625 625 98 12,500.00 57,820.00 70,320.00 1,075.00 625 61250 625 99 12,500.00 58,905.00 71,405.00 1,085.00 625 61875 625Explanation / Answer
When the VC changes from $5 to $3 per unit, the profit keeps increasing with the output and at Q=99 the profit is maximum
Q
FC
VC
TC
MC
P
TR
MR
Profit
0
12500
0
12500
625
0
625
-12500
1
12500
60
12560
60
625
625
625
-11935
2
12500
120
12620
60
625
1250
625
-11370
3
12500
180
12680
60
625
1875
625
-10805
4
12500
240
12740
60
625
2500
625
-10240
5
12500
300
12800
60
625
3125
625
-9675
6
12500
360
12860
60
625
3750
625
-9110
7
12500
420
12920
60
625
4375
625
-8545
8
12500
480
12980
60
625
5000
625
-7980
9
12500
540
13040
60
625
5625
625
-7415
10
12500
600
13100
60
625
6250
625
-6850
11
12500
660
13160
60
625
6875
625
-6285
12
12500
720
13220
60
625
7500
625
-5720
13
12500
780
13280
60
625
8125
625
-5155
14
12500
840
13340
60
625
8750
625
-4590
15
12500
900
13400
60
625
9375
625
-4025
16
12500
960
13460
60
625
10000
625
-3460
17
12500
1020
13520
60
625
10625
625
-2895
18
12500
1080
13580
60
625
11250
625
-2330
19
12500
1140
13640
60
625
11875
625
-1765
20
12500
1200
13700
60
625
12500
625
-1200
21
12500
1260
13760
60
625
13125
625
-635
22
12500
1320
13820
60
625
13750
625
-70
23
12500
1380
13880
60
625
14375
625
495
24
12500
1440
13940
60
625
15000
625
1060
25
12500
1500
14000
60
625
15625
625
1625
26
12500
1560
14060
60
625
16250
625
2190
27
12500
1620
14120
60
625
16875
625
2755
28
12500
1680
14180
60
625
17500
625
3320
29
12500
1740
14240
60
625
18125
625
3885
30
12500
1800
14300
60
625
18750
625
4450
31
12500
1860
14360
60
625
19375
625
5015
32
12500
1920
14420
60
625
20000
625
5580
33
12500
1980
14480
60
625
20625
625
6145
34
12500
2040
14540
60
625
21250
625
6710
35
12500
2100
14600
60
625
21875
625
7275
36
12500
2160
14660
60
625
22500
625
7840
37
12500
2220
14720
60
625
23125
625
8405
38
12500
2280
14780
60
625
23750
625
8970
39
12500
2340
14840
60
625
24375
625
9535
40
12500
2400
14900
60
625
25000
625
10100
41
12500
2460
14960
60
625
25625
625
10665
42
12500
2520
15020
60
625
26250
625
11230
43
12500
2580
15080
60
625
26875
625
11795
44
12500
2640
15140
60
625
27500
625
12360
45
12500
2700
15200
60
625
28125
625
12925
46
12500
2760
15260
60
625
28750
625
13490
47
12500
2820
15320
60
625
29375
625
14055
48
12500
2880
15380
60
625
30000
625
14620
49
12500
2940
15440
60
625
30625
625
15185
50
12500
3000
15500
60
625
31250
625
15750
51
12500
3060
15560
60
625
31875
625
16315
52
12500
3120
15620
60
625
32500
625
16880
53
12500
3180
15680
60
625
33125
625
17445
54
12500
3240
15740
60
625
33750
625
18010
55
12500
3300
15800
60
625
34375
625
18575
56
12500
3360
15860
60
625
35000
625
19140
57
12500
3420
15920
60
625
35625
625
19705
58
12500
3480
15980
60
625
36250
625
20270
59
12500
3540
16040
60
625
36875
625
20835
60
12500
3600
16100
60
625
37500
625
21400
61
12500
3660
16160
60
625
38125
625
21965
62
12500
3720
16220
60
625
38750
625
22530
63
12500
3780
16280
60
625
39375
625
23095
64
12500
3840
16340
60
625
40000
625
23660
65
12500
3900
16400
60
625
40625
625
24225
66
12500
3960
16460
60
625
41250
625
24790
67
12500
4020
16520
60
625
41875
625
25355
68
12500
4080
16580
60
625
42500
625
25920
69
12500
4140
16640
60
625
43125
625
26485
70
12500
4200
16700
60
625
43750
625
27050
71
12500
4260
16760
60
625
44375
625
27615
72
12500
4320
16820
60
625
45000
625
28180
73
12500
4380
16880
60
625
45625
625
28745
74
12500
4440
16940
60
625
46250
625
29310
75
12500
4500
17000
60
625
46875
625
29875
76
12500
4560
17060
60
625
47500
625
30440
77
12500
4620
17120
60
625
48125
625
31005
78
12500
4680
17180
60
625
48750
625
31570
79
12500
4740
17240
60
625
49375
625
32135
80
12500
4800
17300
60
625
50000
625
32700
81
12500
4860
17360
60
625
50625
625
33265
82
12500
4920
17420
60
625
51250
625
33830
83
12500
4980
17480
60
625
51875
625
34395
84
12500
5040
17540
60
625
52500
625
34960
85
12500
5100
17600
60
625
53125
625
35525
86
12500
5160
17660
60
625
53750
625
36090
87
12500
5220
17720
60
625
54375
625
36655
88
12500
5280
17780
60
625
55000
625
37220
89
12500
5340
17840
60
625
55625
625
37785
90
12500
5400
17900
60
625
56250
625
38350
91
12500
5460
17960
60
625
56875
625
38915
92
12500
5520
18020
60
625
57500
625
39480
93
12500
5580
18080
60
625
58125
625
40045
94
12500
5640
18140
60
625
58750
625
40610
95
12500
5700
18200
60
625
59375
625
41175
96
12500
5760
18260
60
625
60000
625
41740
97
12500
5820
18320
60
625
60625
625
42305
98
12500
5880
18380
60
625
61250
625
42870
99
12500
5940
18440
60
625
61875
625
43435
Q
FC
VC
TC
MC
P
TR
MR
Profit
0
12500
0
12500
625
0
625
-12500
1
12500
60
12560
60
625
625
625
-11935
2
12500
120
12620
60
625
1250
625
-11370
3
12500
180
12680
60
625
1875
625
-10805
4
12500
240
12740
60
625
2500
625
-10240
5
12500
300
12800
60
625
3125
625
-9675
6
12500
360
12860
60
625
3750
625
-9110
7
12500
420
12920
60
625
4375
625
-8545
8
12500
480
12980
60
625
5000
625
-7980
9
12500
540
13040
60
625
5625
625
-7415
10
12500
600
13100
60
625
6250
625
-6850
11
12500
660
13160
60
625
6875
625
-6285
12
12500
720
13220
60
625
7500
625
-5720
13
12500
780
13280
60
625
8125
625
-5155
14
12500
840
13340
60
625
8750
625
-4590
15
12500
900
13400
60
625
9375
625
-4025
16
12500
960
13460
60
625
10000
625
-3460
17
12500
1020
13520
60
625
10625
625
-2895
18
12500
1080
13580
60
625
11250
625
-2330
19
12500
1140
13640
60
625
11875
625
-1765
20
12500
1200
13700
60
625
12500
625
-1200
21
12500
1260
13760
60
625
13125
625
-635
22
12500
1320
13820
60
625
13750
625
-70
23
12500
1380
13880
60
625
14375
625
495
24
12500
1440
13940
60
625
15000
625
1060
25
12500
1500
14000
60
625
15625
625
1625
26
12500
1560
14060
60
625
16250
625
2190
27
12500
1620
14120
60
625
16875
625
2755
28
12500
1680
14180
60
625
17500
625
3320
29
12500
1740
14240
60
625
18125
625
3885
30
12500
1800
14300
60
625
18750
625
4450
31
12500
1860
14360
60
625
19375
625
5015
32
12500
1920
14420
60
625
20000
625
5580
33
12500
1980
14480
60
625
20625
625
6145
34
12500
2040
14540
60
625
21250
625
6710
35
12500
2100
14600
60
625
21875
625
7275
36
12500
2160
14660
60
625
22500
625
7840
37
12500
2220
14720
60
625
23125
625
8405
38
12500
2280
14780
60
625
23750
625
8970
39
12500
2340
14840
60
625
24375
625
9535
40
12500
2400
14900
60
625
25000
625
10100
41
12500
2460
14960
60
625
25625
625
10665
42
12500
2520
15020
60
625
26250
625
11230
43
12500
2580
15080
60
625
26875
625
11795
44
12500
2640
15140
60
625
27500
625
12360
45
12500
2700
15200
60
625
28125
625
12925
46
12500
2760
15260
60
625
28750
625
13490
47
12500
2820
15320
60
625
29375
625
14055
48
12500
2880
15380
60
625
30000
625
14620
49
12500
2940
15440
60
625
30625
625
15185
50
12500
3000
15500
60
625
31250
625
15750
51
12500
3060
15560
60
625
31875
625
16315
52
12500
3120
15620
60
625
32500
625
16880
53
12500
3180
15680
60
625
33125
625
17445
54
12500
3240
15740
60
625
33750
625
18010
55
12500
3300
15800
60
625
34375
625
18575
56
12500
3360
15860
60
625
35000
625
19140
57
12500
3420
15920
60
625
35625
625
19705
58
12500
3480
15980
60
625
36250
625
20270
59
12500
3540
16040
60
625
36875
625
20835
60
12500
3600
16100
60
625
37500
625
21400
61
12500
3660
16160
60
625
38125
625
21965
62
12500
3720
16220
60
625
38750
625
22530
63
12500
3780
16280
60
625
39375
625
23095
64
12500
3840
16340
60
625
40000
625
23660
65
12500
3900
16400
60
625
40625
625
24225
66
12500
3960
16460
60
625
41250
625
24790
67
12500
4020
16520
60
625
41875
625
25355
68
12500
4080
16580
60
625
42500
625
25920
69
12500
4140
16640
60
625
43125
625
26485
70
12500
4200
16700
60
625
43750
625
27050
71
12500
4260
16760
60
625
44375
625
27615
72
12500
4320
16820
60
625
45000
625
28180
73
12500
4380
16880
60
625
45625
625
28745
74
12500
4440
16940
60
625
46250
625
29310
75
12500
4500
17000
60
625
46875
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