# Cost Functions by SpreadsheetZONE

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```									COST FUNCTIONS & QUANTITY DECISION
Enter your revenue function, R(q), you may use a polynomial function with up to 4 terms in addition to a fixed term (q is quantity): 3 R(q) 2 1

=

.q

+

-0.01 .q variable

+

1 .q variable

+

20 .q variable

+

Enter your cost function, C(q), you may use a polynomial function with up to 4 terms in addition to a fixed term: 3 C(q) 2 1

=

.q

+

0.02 .q variable

+

0.02 .q variable

+

-25 .q variable

+

150 fixed

Marginal Revenue Function MR(q) = d(R(q)) dq

=

-0.03 .q

2

+

2 .q

+

20

Marginal Cost Function MC(q) = d(C(q)) dq

=

0.06 .q

2

+

0.04 .q

+

-25

Enter the quantity range that you want to simulate: Q(low) = 0 Q(high) = 40

The problem of what quantity to produce is solved by 2 different approaches. Errors due to rounding quantities may exist. The solutions are summarized below: Profit Maximization Approach Marginal Profit Approach q* 36 36 TR 1,549.44 1,549.44 TC 209.04 209.04 TP 1,340.40 1,340.40

PROFIT MAXIMIZATION APPROACH
Rule: Produce at a quantity where maximum profit is observed. TC = Total Cost TR = Total Revenue
2000

Pmax = maximum profit observed

1500

1000

TC TR
Pmax

500

0 0 -500 5 10 15 20 25 30 35 40 45

Maximum profit, 1340,is achieved at quantity 36.

MARGINAL PROFIT APPROACH
Rule: Produce at a quantity where marginal revenue is equal to marginal cost. MR = Marginal Revenue MC = Marginal Cost
80 60
40

20 0 0 -20 -40 5 10 15 20 25 30 35 40 45

MR MC

MR and MC are equal, 53.12, at quantity 36.

1 Index 0 1E-10 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 36 36 37 37 38 38 39 39 40 40

Fixed Cost 150 0 0 0 0 150

Fixed Cost Chart Var Cost 1 Var Cost 2 Var Cost 3 Var Cost 4 Var Cost 0 40 0 2E-32 2E-22 -2.5E-09 -2.5E-09 150 150 0 0.02 0.02 -25 -24.96 0 0.16 0.08 -50 -49.76 0 0.54 0.18 -75 -74.28 0 1.28 0.32 -100 -98.4 0 2.5 0.5 -125 -122 0 4.32 0.72 -150 -144.96 0 6.86 0.98 -175 -167.16 0 10.24 1.28 -200 -188.48 0 14.58 1.62 -225 -208.8 0 20 2 -250 -228 0 26.62 2.42 -275 -245.96 0 34.56 2.88 -300 -262.56 0 43.94 3.38 -325 -277.68 0 54.88 3.92 -350 -291.2 0 67.5 4.5 -375 -303 0 81.92 5.12 -400 -312.96 0 98.26 5.78 -425 -320.96 0 116.64 6.48 -450 -326.88 0 137.18 7.22 -475 -330.6 0 160 8 -500 -332 0 185.22 8.82 -525 -330.96 0 212.96 9.68 -550 -327.36 0 243.34 10.58 -575 -321.08 0 276.48 11.52 -600 -312 0 312.5 12.5 -625 -300 0 351.52 13.52 -650 -284.96 0 393.66 14.58 -675 -266.76 0 439.04 15.68 -700 -245.28 0 487.78 16.82 -725 -220.4 0 540 18 -750 -192 0 595.82 19.22 -775 -159.96 0 655.36 20.48 -800 -124.16 0 718.74 21.78 -825 -84.48 0 786.08 23.12 -850 -40.8 0 857.5 24.5 -875 7 0 933.12 25.92 -900 59.04 0 1013.06 27.38 -925 115.44 0 1097.44 28.88 -950 176.32 0 1186.38 30.42 -975 241.8 0 1280 32 -1000 312

TC 150 125.04 100.24 75.72 51.6 28 5.04 -17.16 -38.48 -58.8 -78 -95.96 -112.56 -127.68 -141.2 -153 -162.96 -170.96 -176.88 -180.6 -182 -180.96 -177.36 -171.08 -162 -150 -134.96 -116.76 -95.28 -70.4 -42 -9.96 25.84 65.52 109.2 157 209.04 265.44 326.32 391.8 462

MC 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

MC 2 6E-22 0.06 0.24 0.54 0.96 1.5 2.16 2.94 3.84 4.86 6 7.26 8.64 10.14 11.76 13.5 15.36 17.34 19.44 21.66 24 26.46 29.04 31.74 34.56 37.5 40.56 43.74 47.04 50.46 54 57.66 61.44 65.34 69.36 73.5 77.76 82.14 86.64 91.26 96

MC 3 4E-12 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4 0.44 0.48 0.52 0.56 0.6 0.64 0.68 0.72 0.76 0.8 0.84 0.88 0.92 0.96 1 1.04 1.08 1.12 1.16 1.2 1.24 1.28 1.32 1.36 1.4 1.44 1.48 1.52 1.56 1.6

MC 4 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25

MC Revenue 1 Revenue 2 Revenue 3 Revenue 4 0 -1E-32 1E-20 0.000000002 -24.9 0 -0.01 1 20 -24.68 0 -0.08 4 40 -24.34 0 -0.27 9 60 -23.88 0 -0.64 16 80 -23.3 0 -1.25 25 100 -22.6 0 -2.16 36 120 -21.78 0 -3.43 49 140 -20.84 0 -5.12 64 160 -19.78 0 -7.29 81 180 -18.6 0 -10 100 200 -17.3 0 -13.31 121 220 -15.88 0 -17.28 144 240 -14.34 0 -21.97 169 260 -12.68 0 -27.44 196 280 -10.9 0 -33.75 225 300 -9 0 -40.96 256 320 -6.98 0 -49.13 289 340 -4.84 0 -58.32 324 360 -2.58 0 -68.59 361 380 -0.2 0 -80 400 400 2.3 0 -92.61 441 420 4.92 0 -106.48 484 440 7.66 0 -121.67 529 460 10.52 0 -138.24 576 480 13.5 0 -156.25 625 500 16.6 0 -175.76 676 520 19.82 0 -196.83 729 540 23.16 0 -219.52 784 560 26.62 0 -243.89 841 580 30.2 0 -270 900 600 33.9 0 -297.91 961 620 37.72 0 -327.68 1024 640 41.66 0 -359.37 1089 660 45.72 0 -393.04 1156 680 49.9 0 -428.75 1225 700 54.2 0 -466.56 1296 720 58.62 0 -506.53 1369 740 63.16 0 -548.72 1444 760 67.82 0 -593.19 1521 780 72.6 0 -640 1600 800

Fixed Revenue Revenue Profit 0 2E-09 -150 0 20.99 -104.05 0 43.92 -56.32 0 68.73 -6.99 0 95.36 43.76 0 123.75 95.75 153.84 148.8 185.57 202.73 218.88 257.36 253.71 312.51 290 368 327.69 423.65 366.72 479.28 407.03 534.71 448.56 589.76 491.25 644.25 535.04 698 579.87 750.83 625.68 802.56 672.41 853.01 720 902 768.39 949.35 817.52 994.88 867.33 1038.41 917.76 1079.76 968.75 1118.75 1020.24 1155.2 1072.17 1188.93 1124.48 1219.76 1177.11 1247.51 1230 1272 1283.09 1293.05 1336.32 1310.48 1389.63 1324.11 1442.96 1333.76 1496.25 1339.25 1549.44 1340.4 1602.47 1337.03 1655.28 1328.96 1707.81 1316.01 1760 1298

1340.4 36 36

209.04 1549.44

MR 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

MR 2 -3E-22 -0.03 -0.12 -0.27 -0.48 -0.75 -1.08 -1.47 -1.92 -2.43 -3 -3.63 -4.32 -5.07 -5.88 -6.75 -7.68 -8.67 -9.72 -10.83 -12 -13.23 -14.52 -15.87 -17.28 -18.75 -20.28 -21.87 -23.52 -25.23 -27 -28.83 -30.72 -32.67 -34.68 -36.75 -38.88 -41.07 -43.32 -45.63 -48

MR 3 2E-10 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80

MR 4 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20

MR 21.97 23.88 25.73 27.52 29.25 30.92 32.53 34.08 35.57 37 38.37 39.68 40.93 42.12 43.25 44.32 45.33 46.28 47.17 48 48.77 49.48 50.13 50.72 51.25 51.72 52.13 52.48 52.77 53 53.17 53.28 53.33 53.32 53.25 53.12 52.93 52.68 52.37 52 46.87 48.56 50.07 51.4 52.55 53.52 54.31 54.92 55.35 55.6 55.67 55.56 55.27 54.8 54.15 53.32 52.31 51.12 49.75 48.2 46.47 44.56 42.47 40.2 37.75 35.12 32.31 29.32 26.15 22.8 19.27 15.56 11.67 7.6 3.35 -1.08 -5.69 -10.48 -15.45 -20.6 46.87 48.56 50.07 51.4 52.55 53.52 54.31 54.92 55.35 55.6 55.67 55.56 55.27 54.8 54.15 53.32 52.31 51.12 49.75 48.2 46.47 44.56 42.47 40.2 37.75 35.12 32.31 29.32 26.15 22.8 19.27 15.56 11.67 7.6 3.35 1.08 5.69 10.48 15.45 20.6

1.08 36

53.12

TRUE 40

Follow the steps to enable your Cost Functions template.
>> 2 approaches are used to find the find the optimal production quantity that results in the maximum profit: >>

This template is prepared for assisting the decision of production volume. The template can handle polynomial revenue and cost fun

Your Cost Functions template is ready to use. Following steps are for online use. Total Profit Approach and Marginal Profit Approach are calculated and summarized on a table.

Copyright (c) 2009 Pagos, Inc. http://www.pagos.com/

lynomial revenue and cost functions up to degree 5.

and Marginal Profit Approach. Both approaches are expected

roducts may exist. Hence, both approaches and their results

f-97b7-18fe1f165087

```
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