Problem 10-15 The Camera Shop sells two popular models of digital SLR cameras (C

Question

Problem 10-15 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 -190 0.7PA 0.35Ps Ns = 300 + 0.07Pa-0.6ps 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 S Max profit occurs at Camera B price of

Explanation / Answer

Maximum Profit = 84999 Price of the Product A = 270 Price of the Product B = 390 Revenue at different prices of A and B (in $'s) Price of B, PB 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 Prices of A, PA 250 75875 77160 78345 79430 80415 81300 82085 82770 83355 83840 84225 84510 84695 84780 84765 84650 84435 84120 83705 83190 82575 81860 81045 80130 79115 78000 260 75590 76908 78126 79244 80262 81180 81998 82716 83334 83852 84270 84588 84806 84924 84942 84860 84678 84396 84014 83532 82950 82268 81486 80604 79622 78540 270 75185 76536 77787 78938 79989 80940 81791 82542 83193 83744 84195 84546 84797 84948 84999 84950 84801 84552 84203 83754 83205 82556 81807 80958 80009 78960 280 74660 76044 77328 78512 79596 80580 81464 82248 82932 83516 84000 84384 84668 84852 84936 84920 84804 84588 84272 83856 83340 82724 82008 81192 80276 79260 290 74015 75432 76749 77966 79083 80100 81017 81834 82551 83168 83685 84102 84419 84636 84753 84770 84687 84504 84221 83838 83355 82772 82089 81306 80423 79440 300 73250 74700 76050 77300 78450 79500 80450 81300 82050 82700 83250 83700 84050 84300 84450 84500 84450 84300 84050 83700 83250 82700 82050 81300 80450 79500 310 72365 73848 75231 76514 77697 78780 79763 80646 81429 82112 82695 83178 83561 83844 84027 84110 84093 83976 83759 83442 83025 82508 81891 81174 80357 79440 320 71360 72876 74292 75608 76824 77940 78956 79872 80688 81404 82020 82536 82952 83268 83484 83600 83616 83532 83348 83064 82680 82196 81612 80928 80144 79260 330 70235 71784 73233 74582 75831 76980 78029 78978 79827 80576 81225 81774 82223 82572 82821 82970 83019 82968 82817 82566 82215 81764 81213 80562 79811 78960 340 68990 70572 72054 73436 74718 75900 76982 77964 78846 79628 80310 80892 81374 81756 82038 82220 82302 82284 82166 81948 81630 81212 80694 80076 79358 78540 350 67625 69240 70755 72170 73485 74700 75815 76830 77745 78560 79275 79890 80405 80820 81135 81350 81465 81480 81395 81210 80925 80540 80055 79470 78785 78000 360 66140 67788 69336 70784 72132 73380 74528 75576 76524 77372 78120 78768 79316 79764 80112 80360 80508 80556 80504 80352 80100 79748 79296 78744 78092 77340 370 64535 66216 67797 69278 70659 71940 73121 74202 75183 76064 76845 77526 78107 78588 78969 79250 79431 79512 79493 79374 79155 78836 78417 77898 77279 76560 380 62810 64524 66138 67652 69066 70380 71594 72708 73722 74636 75450 76164 76778 77292 77706 78020 78234 78348 78362 78276 78090 77804 77418 76932 76346 75660 390 60965 62712 64359 65906 67353 68700 69947 71094 72141 73088 73935 74682 75329 75876 76323 76670 76917 77064 77111 77058 76905 76652 76299 75846 75293 74640 400 59000 60780 62460 64040 65520 66900 68180 69360 70440 71420 72300 73080 73760 74340 74820 75200 75480 75660 75740 75720 75600 75380 75060 74640 74120 73500 410 56915 58728 60441 62054 63567 64980 66293 67506 68619 69632 70545 71358 72071 72684 73197 73610 73923 74136 74249 74262 74175 73988 73701 73314 72827 72240 420 54710 56556 58302 59948 61494 62940 64286 65532 66678 67724 68670 69516 70262 70908 71454 71900 72246 72492 72638 72684 72630 72476 72222 71868 71414 70860 430 52385 54264 56043 57722 59301 60780 62159 63438 64617 65696 66675 67554 68333 69012 69591 70070 70449 70728 70907 70986 70965 70844 70623 70302 69881 69360 440 49940 51852 53664 55376 56988 58500 59912 61224 62436 63548 64560 65472 66284 66996 67608 68120 68532 68844 69056 69168 69180 69092 68904 68616 68228 67740 450 47375 49320 51165 52910 54555 56100 57545 58890 60135 61280 62325 63270 64115 64860 65505 66050 66495 66840 67085 67230 67275 67220 67065 66810 66455 66000 460 44690 46668 48546 50324 52002 53580 55058 56436 57714 58892 59970 60948 61826 62604 63282 63860 64338 64716 64994 65172 65250 65228 65106 64884 64562 64140 470 41885 43896 45807 47618 49329 50940 52451 53862 55173 56384 57495 58506 59417 60228 60939 61550 62061 62472 62783 62994 63105 63116 63027 62838 62549 62160 480 38960 41004 42948 44792 46536 48180 49724 51168 52512 53756 54900 55944 56888 57732 58476 59120 59664 60108 60452 60696 60840 60884 60828 60672 60416 60060 490 35915 37992 39969 41846 43623 45300 46877 48354 49731 51008 52185 53262 54239 55116 55893 56570 57147 57624 58001 58278 58455 58532 58509 58386 58163 57840 500 32750 34860 36870 38780 40590 42300 43910 45420 46830 48140 49350 50460 51470 52380 53190 53900 54510 55020 55430 55740 55950 56060 56070 55980 55790 55500

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