Explain why the linear programming problem has an optimal solution, and find it using the table method.
Maximize P = 15x + 30X2
subject to - 4x4 + x2 s 20
X, S 50
Xy, xz 20
Explain why the linear programming problem has an optimal solution.
1f (X4 X2) is a point in the feasible region, then 0 sxy s 50 and 0 sxs 220. Thus, the feasible region is bounded.
(Simplify your answers.)
Find the optimal solution. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
O A The function is maximized when x2 = 50 and x2 = 220), where P = 7,350
(Simplify your answers.)
B. The system has no optimal solution.

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?