In a linear programming problem, where is the optimal (maximum or minimum) value of the objective function always found?

Along the edges of the feasible region

At one of the vertices of the feasible region

Inside the center of the feasible region

A bakery can make at most 30 items (cakes, $c$, and pies, $p$) per day. Each cake costs 12 dollars to make and each pie costs 8 dollars. The daily budget is no more than 300 dollars. Which inequalities represent these constraints?

$c + p \geq 30, 12c + 8p \geq 300, c \geq 0, p \geq 0$

$c + p \leq 30, 12c + 8p \leq 300, c \geq 0, p \geq 0$

$c + p \leq 30, 12c + 8p \leq 300$

$t + h \leq 200, 3t + 2h \geq 900, t \geq 0, h \geq 0$

$t + h \geq 200, 3t + 2h \leq 900$

$t + h \geq 200, 3t + 2h \leq 900, t \geq 0, h \geq 0$

$t + h \leq 200, 3t + 2h \leq 900, t \geq 0, h \geq 0$