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5 October, 17:40

The Camera Shop sells two popular models of digital SLR cameras (Camera A Price: 200, Camera A Price: 300). The sales of these products are not independent of each other, but rather if the price of one increase, the sales of the other will increase. In economics, these two camera models are called substitutable products. The store wishes to establish a pricing policy to maximize revenue from these products. A study of price and sales data shows the following relationships between the quantity sold (N) and prices (P) of each model:

NA = 195 - 0.5PA + 0.35PB

NB = 300 + 0.06PA - 0.5PB

Construct a model for the total revenue and implement it on a spreadsheet. Develop two-way data table to estimate the optimal prices for each product in order to maximize the total revenue. Vary each price from $250 to $500 in increments of $10.

Max profit occurs at Camera A price of $.

Max profit occurs at Camera B price of $

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  1. 5 October, 18:40
    0
    Max Revenue (not necessarily profit) occurs at Camera A price of $380

    Max Revenue (not necessarily profit) occurs at Camera B price of $460

    Explanation:

    Assuming prices varying between $250 to $500 with $10 intervals, the total revenues of camera A are shown below:

    Statement showing maximum reveue of Camera A

    Price - A 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500

    Price B

    250 26875 26390 25785 25060 24215 23250 22165 20960 19635 18190 16625 14940 13135 11210 9165 7000 4715 2310 - 215 - 2860 - 5625 - 8510 - 11515 - 14640 - 17885 - 21250

    260 27500 27040 26460 25760 24940 24000 22940 21760 20460 19040 17500 15840 14060 12160 10140 8000 5740 3360 860 - 1760 - 4500 - 7360 - 10340 - 13440 - 16660 - 20000

    270 28125 27690 27135 26460 25665 24750 23715 22560 21285 19890 18375 16740 14985 13110 11115 9000 6765 4410 1935 - 660 - 3375 - 6210 - 9165 - 12240 - 15435 - 18750

    280 28750 28340 27810 27160 26390 25500 24490 23360 22110 20740 19250 17640 15910 14060 12090 10000 7790 5460 3010 440 - 2250 - 5060 - 7990 - 11040 - 14210 - 17500

    290 29375 28990 28485 27860 27115 26250 25265 24160 22935 21590 20125 18540 16835 15010 13065 11000 8815 6510 4085 1540 - 1125 - 3910 - 6815 - 9840 - 12985 - 16250

    300 30000 29640 29160 28560 27840 27000 26040 24960 23760 22440 21000 19440 17760 15960 14040 12000 9840 7560 5160 2640 0 - 2760 - 5640 - 8640 - 11760 - 15000

    310 30625 30290 29835 29260 28565 27750 26815 25760 24585 23290 21875 20340 18685 16910 15015 13000 10865 8610 6235 3740 1125 - 1610 - 4465 - 7440 - 10535 - 13750

    320 31250 30940 30510 29960 29290 28500 27590 26560 25410 24140 22750 21240 19610 17860 15990 14000 11890 9660 7310 4840 2250 - 460 - 3290 - 6240 - 9310 - 12500

    330 31875 31590 31185 30660 30015 29250 28365 27360 26235 24990 23625 22140 20535 18810 16965 15000 12915 10710 8385 5940 3375 690 - 2115 - 5040 - 8085 - 11250

    340 32500 32240 31860 31360 30740 30000 29140 28160 27060 25840 24500 23040 21460 19760 17940 16000 13940 11760 9460 7040 4500 1840 - 940 - 3840 - 6860 - 10000

    350 33125 32890 32535 32060 31465 30750 29915 28960 27885 26690 25375 23940 22385 20710 18915 17000 14965 12810 10535 8140 5625 2990 235 - 2640 - 5635 - 8750

    360 33750 33540 33210 32760 32190 31500 30690 29760 28710 27540 26250 24840 23310 21660 19890 18000 15990 13860 11610 9240 6750 4140 1410 - 1440 - 4410 - 7500

    370 34375 34190 33885 33460 32915 32250 31465 30560 29535 28390 27125 25740 24235 22610 20865 19000 17015 14910 12685 10340 7875 5290 2585 - 240 - 3185 - 6250

    380 35000 34840 34560 34160 33640 33000 32240 31360 30360 29240 28000 26640 25160 23560 21840 20000 18040 15960 13760 11440 9000 6440 3760 960 - 1960 - 5000

    390 35625 35490 35235 34860 34365 33750 33015 32160 31185 30090 28875 27540 26085 24510 22815 21000 19065 17010 14835 12540 10125 7590 4935 2160 - 735 - 3750

    400 36250 36140 35910 35560 35090 34500 33790 32960 32010 30940 29750 28440 27010 25460 23790 22000 20090 18060 15910 13640 11250 8740 6110 3360 490 - 2500

    410 36875 36790 36585 36260 35815 35250 34565 33760 32835 31790 30625 29340 27935 26410 24765 23000 21115 19110 16985 14740 12375 9890 7285 4560 1715 - 1250

    420 37500 37440 37260 36960 36540 36000 35340 34560 33660 32640 31500 30240 28860 27360 25740 24000 22140 20160 18060 15840 13500 11040 8460 5760 2940 0

    430 38125 38090 37935 37660 37265 36750 36115 35360 34485 33490 32375 31140 29785 28310 26715 25000 23165 21210 19135 16940 14625 12190 9635 6960 4165 1250

    440 38750 38740 38610 38360 37990 37500 36890 36160 35310 34340 33250 32040 30710 29260 27690 26000 24190 22260 20210 18040 15750 13340 10810 8160 5390 2500

    450 39375 39390 39285 39060 38715 38250 37665 36960 36135 35190 34125 32940 31635 30210 28665 27000 25215 23310 21285 19140 16875 14490 11985 9360 6615 3750

    460 40000 40040 39960 39760 39440 39000 38440 37760 36960 36040 35000 33840 32560 31160 29640 28000 26240 24360 22360 20240 18000 15640 13160 10560 7840 5000

    470 40625 40690 40635 40460 40165 39750 39215 38560 37785 36890 35875 34740 33485 32110 30615 29000 27265 25410 23435 21340 19125 16790 14335 11760 9065 6250

    480 41250 41340 41310 41160 40890 40500 39990 39360 38610 37740 36750 35640 34410 33060 31590 30000 28290 26460 24510 22440 20250 17940 15510 12960 10290 7500

    490 41875 41990 41985 41860 41615 41250 40765 40160 39435 38590 37625 36540 35335 34010 32565 31000 29315 27510 25585 23540 21375 19090 16685 14160 11515 8750

    500 42500 42640 42660 42560 42340 42000 41540 40960 40260 39440 38500 37440 36260 34960 33540 32000 30340 28560 26660 24640 22500 20240 17860 15360 12740 10000

    Max Revenue (not necessarily profit) occurs at Camera A price of $380

    Max Revenue (not necessarily profit) occurs at Camera B price of $460
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