(1) If the mall buys both A and B products at the same time *** 100, it is exactly 2700 yuan. How many items a and b can it buy? Let a be x and b be y x+y =10015x+35y = 2700. The solution is: X=40, Y=60 (2). The total profit (profit = selling price +000 pieces) of A and B in the shopping mall is designed: X pieces of A and (100-X) pieces of B are purchased.

Profit W=5X+ 10( 100-X)

According to the meaning, we can get 750 ≤ 5x+10 (100-x) ≤ 760.

The solution is x=48≤X≤50, so a is: x = 48,49,50b is: 52,565,438+0,50.

There are three purchase plans.

① A 48 B 52

② A 49 B 5 1

③ A 50 B 50

(The most profitable option is Option 1)

(3) Day 1: No discount. Therefore, to buy a commodity: 200÷20= 10 (piece)

The next day: discount.

①324÷0.9=360 (yuan) for the second commodity: 360÷45=8 (pieces).

* * * Bought 18 items from Party A and Party B. ..

②324÷0.8=405 (yuan)

405÷45=9 (pieces)

So * * * bought 19 items from both parties.