MCV4U0 - Unit 4 Optimization / 70 NAME: Provide a FULL solution with all your steps. 1.3.x 1.3.x 1)The given figure is made up of an isosceles triangle on top of a rectangle. If the perimeter is 48 m, determine the exact value (no decimal answer) of x that produces a maximum area. 2)Find the maximum perimeter possible (in exact form) for a right angled triangle with hypotenuse of atcm. 3) A swimming competition has a contestant swimming from a point on one shore of a Sandy lake to another point on the opposite parallel shore, then running to the finish line further along the shore. The lake is 5 km wide, and the finish line is 12 km down the lake. If a contestant can swim at 3 km/h and run at 12 km/h, determine the location of the point on the opposite side of the lake where they should finish swimming to minimize the total time for the race. 4) What will be the minimum cost to install a cylinder of volume 950 cm in a rectangular prism with length of 11 cm, width of 14 cm and height of 10 cm. The cost to construct the top of the cylinder is $80/cm?, base of the cylinder is $80/cm and the wall ( sides) is $45/cm . 5. Lawrie, Gavin, and Alan are building a shed in the shape of a rectangular prism. The volume of the shed is given by VXx) - 108x - 27x" + 2X" , where x is the height of the shed in metres, for 0