You have a budget $B$ and a satisfaction level $L$. An indivisible product is available for sell and you are interested in buying. The product is divided into $n$ parts. Part $i$ of the product has positive value $v_i$.
On day $i$, you get to know $v_i$ and you have to decide how much price $p_i\geq0$ you would pay for this part of the product.
After $j$ days, given the values $v_1, v_2, \ldots, v_j$ and the prices you paid $p_1, p_2, \ldots, p_j$ for each value, you know that you can reach a satisfaction level of $(1+v_1p_1)(1+v_2p_2)\cdots(1+v_jp_j)$.
Your objective is to buy the product after $n$ days while you reach the satisfaction level of $L$ and pay no more than $B$.