please answer ALL QUESTIONS so that i may rate you thumbs up 9. A copper sheet with 16 cm by 16 cm dimension has to be made as a square boxwith no top cover. Square corners should have cut outs to enable folding of everyside. Find the dimensions of the box that will give the maximum volume.A. I and w =32cm, height 8/3cm%3D16B. I and w =cm, height = -33cmC. I and w =3cm, height = 5/3cmD. I and w cm, height = 2/3cm%3D10. A carton board with 50 in by 50 in dimension has to be made as a square boxwith no top cover. Square corners should have cut outs to enable folding ofevery side. Find the dimensions of the box that will give the maximum volume.A. I and w =105cm, height = 24/3cm399B. I and w =cm, height = 23/3cm%3D100C. I and w =cm, height = 25/3cmD. I and w =110cm, height = 22/3cm3 Solve the following word problems. Write your answer on a separate sheet of paper.1. Look for two numbers with a difference of 6 such that the product is a minimum.A. 10 and 4B. 12, and 6С. З апd - 3D. 2 and 82. Variables a and b represent two positive numbers such that a + b2 = 1. Find thesetwo numbers that will maximize the equation, P = ab?.A. a =,b =V3B. a = ,bV5C. a = .b =D. a = b =%3D3. Look for two numbers with a difference of 12 such that the product is a minimum.A. 6 and - 6B. 12, and 24C. 3 and 15D. 7 and 84. Variables a and b represent two positive numbers such that a + b2 = 4. Find thesetwo numbers that will maximize the equation, P = ab?.A. a = 2, b = V2B. a = 3, b = V2C. a = 2, b = 3D. a = 4, b = 25. Find two numbers with a sum of S so that the equation S = 2x? + 3y? will give aminimum value.A. 6 and – 6В. З апd 2С. 1 аnd 4D. -2 and 86. Solve for the dimensions of the rectangle with a perimeter of 450 m such that thearea is a maximum.A. 50m and 10mС. 35m and 25mВ. 20т ипd 40D. 112.5m and 112.5mFind two numbers with a sum of 3 so that the equation S = x² + 2y? will give aminimum value.A. 6 and - 5В. 1, and 4С. З аnd 1D. 2 and 18. Lito wants to fence his subdivision lot. He wants to install fences on itsrectangular region and maximize the area. He measured and found out that itsperimeter is 280 m. What are the dimensions of the rectangular region that willgive him the maximum area possible?А. 120т аnd 10mC. 35m and 25mD. 70m and 70mB. 25m and 80m

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Look for two numbers with a difference of 6 such that the product is a minimum. A. 10 and 4 В. 12, аnd 6 С. З апd - 3 D. 2 and 8