4. Maximize : Z =10x+30y Subject to: 2x+ y 2 16 x+y <12 x+2y 214 х, у 20

24. * A company wants to purchase a rectangular advertisement space in a magazine. The magazine re- quires that the top and bottom margins (2cm each), as well as the side margins (1cm each) of the space be left completely blank. The area of the space offered, including the margins, is 72 square centime- ters. What dimensions should the company request for its advertisement (including the margins) to maximize the printed area?

6. A family wants to build a fence in their backyard for their dogs, Charlie and Linus. The enclosed space needs to be a rectangle with an area of 4000 square meters. One side of the enclosed space will be next to the house, so they only need fencing along three sides of the rectangle. How much fencing will they need to buy to minimize the perimeter of the enclosed space?

2. The volume of a cylinder is given by (πx^3+4x^2-3x -18π) сm3. If the radius of the cylinder is (x+3) cm, determine the height of the cylinder in terms of x. Option 1 h =(x - 5) cm O Option 2 h =(x −15) cm O Option 3 h =(x +2) cm O Option 4 h =(x-2) cm

34. 2t √ ₁²+2t+10 dt t² + 2t + 10