Problem 7-15 The Camera Shop sells two popular models of digital cameras. The sa
ID: 466940 • Letter: P
Question
Problem 7-15
The Camera Shop sells two popular models of digital cameras. 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 = 192 - 0.5PA + 0.25PB
NB = 305 + 0.08PA - 0.6PB
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 $ .
Explanation / Answer
Lets assume the cost of Camera A is $250 when Camera B $ 500 because demands will be inversely proportional for the prices. Lets increase the price of camera A by $ 10 and decrease the price of camera B by $10 to see how the demand changes for both.
Considering the below formulas to determine the demand of each products for every change in price , the table is constructed below'
Below tabe shows the revenue will be maximum when price of camera A is $360 and Camera B is $390. The max revenue is $78342 . The demand of camera A is 110 units and Camera B is 100 units.
Also Max profit occurs art Camera A at price of $250 i.e. $48000
Max profit occurs at Camera B at proce of $270. i.e $48978
PA PB NA = 192 - 0.5PA + 0.25PB NB = 305 + 0.08PA - 0.6PB Revenue on A Revenue on B Total Revenue 250 500 192 25 48000 12500 60500 260 490 185 32 47970 15582 63552 270 480 177 39 47790 18528 66318 280 470 170 45 47460 21338 68798 290 460 162 52 46980 24012 70992 300 450 155 59 46350 26550 72900 310 440 147 66 45570 28952 74522 320 430 140 73 44640 31218 75858 330 420 132 79 43560 33348 76908 340 410 125 86 42330 35342 77672 350 400 117 93 40950 37200 78150 360 390 110 100 39420 38922 78342 370 380 102 107 37740 40508 78248 380 370 95 113 35910 41958 77868 390 360 87 120 33930 43272 77202 400 350 80 127 31800 44450 76250 410 340 72 134 29520 45492 75012 420 330 65 141 27090 46398 73488 430 320 57 147 24510 47168 71678 440 310 50 154 21780 47802 69582 450 300 42 161 18900 48300 67200 460 290 35 168 15870 48662 64532 470 280 27 175 12690 48888 61578 480 270 20 181 9360 48978 58338 490 260 12 188 5880 48932 54812 500 250 5 195 2250 48750 51000