You have sufficient budget next month to buy a total of 10 ads spread across 6 different regions, with each ad costs $0.5 million. Your company's marketing analytics team have prepared a study predicting that the net sales (in millions of dollars) in region t should be well estimated by the formula

S_t = A_t - B_t exp(-C_td)

Where d is the number of ads purchased in region t, and A_t, B_t, and C_t are constants as specified in the following table

Region (t)	1	2	3	4	5	6
At	4.1	8.2	6.9	2.3	4.4	5.2
Bt	2.1	4.3	3.2	1.9	2.2	3.1
Ct	0.4	0.3	0.2	0.6	0.4	0.3

You would like to maximize your total predicted profit, which is the sum of the predicted net sales from all regions, minus the amount spent purchasing ads. You do not have to place all 10 possible ads.

Note: if you place the command import math at the start of your program, the mathematical function exp(x) = e^x may be accessed through the Python expression math.exp(x).

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