Question: A camping supply company makes backpacks in two models, journey and trek. The journey model requires $4$ hours of labor and generates a profit of $40$ dollars. The trek model requires $6$ hours of labor and generates a profit of $80$ dollars. The company needs to profit at least $\$400$ per week. Their distributor will accept no more than $4$ trek backpacks and no more than $15$ journey backpacks per week. How many of each type of backpack should the company make to minimize the number of hours of labor?
I let $x$ be the number journey and $y$ be the number of trek backpacks produced during the week. Thus, we have
$$40x+80y\geq 400\\0\leq x\leq 4\\ 0\leq y\leq 15\tag1$$
And an objective function of $4x+6y$. Thus, the minimized/maximized points are $(0,5),(0,15),(4,3),(4,15)$ and I got $0,5$ as the answer. Meaning $5$ treks and no journeys.
But the problem was wrong. It was supposed to be $(4,3)$.
Where did I go wrong?