Consider the LPP

Maximize: Z= 5x+3y subject to constraints

$2x+5y ≤15; 5x +2y ≤ 10; x, y ≥0.$ Which of the following is true ?

A. The feasible region lies in the $1^{st}$ quadrant.

B. The maximum value of 9.

C. The feasible region has 4 corner points.

D. It has three optimal solutions.

E. The maximum value of Z lies at $\left(\frac{20}{19}, \frac{45}{19}\right) $ and $(2, 0)$

Choose the correct answer from the options given below :

A, C, E only

The correct answer is Option (4) → A, C, E only

(A) Yes, the feasible region lies in Ist quadrant $(x,y≥0)$

(C) Yes, the feasible region has four corner points name 0, A, B, C

(E) $Z_{max}\left(\frac{20}{19}, \frac{45}{19}\right) =Z_{max}(2, 0)$

$5×2+3×0=5×\frac{20}{19}+3×\frac{45}{19}$

$10=10$