Solve the following linear programming problem using the method of corners: Minimize P= 58x + 45y Objective: Subject to: I- y<-5 3x – 8y < -30 x> -2, y < 8 Enter DNE for each blank if such a value does not exist. If there are infinitely many solutions, list the two corner points on the corresponding line segment with a comma between them. The minimum of P = 58r + 45y is and occurs?

Draw the graph of y = 3x2 + 6x − 24 and label its minimum.

Kk.312.

In this question, you will work step-by-step through an optimization problem. Many airlines restrict the size of carry on item in terms of their combined length, width and height (L+W+H). I am due to fly on an airline that states "The sum of the length, the width and height of your item must be at most 50 inches". Suppose I want to take a box (cuboid) on my trip that will allow me to carry on as much as possible, and that I also want this box to have a square base. The questions we will answer using optimization are: What dimensions should the box have, and what would be the resulting maximum volume? If the base of the box is a square whose sides have length x, and the height of the box is h (both measured in inches), enter expressions for the volume of the box, V, and the sum of the length, width and height of the box in terms of x and h. V :  Sum L+W+H :    Since the sum of the length, width and height must be less than or equal to 50 inches, and it is clearly best to choose this…