Modeling Questions

Rate of growth of bacteria is proportional to the number of bacteria present at time. If $x$ is the number of bacteria present at any instant $t$, then which one of the following is correct? (Let the proportional constant equal to $2$)

Ram is a fruit seller. Apples cost Rs 80/kg and Mangoes Rs 120/kg. Profits are Rs 10/kg and Rs 12/kg respectively. Let $x$ be kgs of apples and $y$ be kgs of mangoes. If Ram wants to maximize profit, the objective function $Z$ is: