Which of the following are true and which are false? explain your answers.

(i) there exists an lp with exactly two optimal solutions. (ii) there exists an lp with exactly two optimal corner solutions. (iii) if an lp is feasible, then it has an optimal solution that is a corner point. (iv) consider an lp with m constraints and n variables. we can transform it into an equivalent lp in standard form with at most 2m + 2n constraints and 2n + m variables.

you could deduce the conclusion directly using the facts pertaining to the specific situation.

hope this .

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west

he is going to fill two shelves and the third shelf will only have five video games