Question

please only answer if willing to answer all thank you!

A rectangular poster is to contain 968 square Inches of print. The margins at the top and bottom of the poster are to be 2 inches, and the margins on the left and right are to be 1 inch What should the dimensions of the poster be so that the least amount of poster is used in smaller value in larger value Need Help

Answer 1

First Question Solution: Suppose dimensions of printed poster are x inch and y inch. Then, Area =X X y square inches According to question, Area of printed poster= 968 square inches - xy = 968 ...... (1) 2 inch 968 968 square inches lindhes y = ... (2) 1 inch x inch After taking margins into account, we get Area of poster = (x + 4) (y + 2) = xy + 4y + 2x + 8 = 968 + 4y + 2x +8 2 from (i) = xy = 968 = 976 + 4y + 2x 968 3872 =976 + + 2x from (ii) y = So we can write Area of poster as function of x, A(x) say 3872 A(x) = 976 + + 2x 3872 · A'(x) = - 12 + 2 For least area of poster evaluate A'(x) = 0, we get 3872 x = 1936 x= V1936 = 44 968 - from (ii), y = 968 = 22 44 Thus, for least amount of poster dimension's will be 44 inch and 22 inch. Note: (i)you should know Chege policy. (il) all other questions are based on first question, So please go through this solution.

Q6 Solution: Suppose dimensions of rectangular pasture are x inch and y inch. Then, Area =x x y square inches According to question, Area of rectangular pasture = 180,000 square inches :: xy = 180,000 ... (1) 180,000 > y = ...... (2) y inch 180,000 square inches y inch x inch Perimeter of rectangular pasture = x + 2y So we can write Perimeter of rectangular pasture as function of x, P(x) say 180,000 P(x) = x + 2 x 360,000 .:P'(x) = 1 - x2 For least Perimeter of rectangular pasture , evaluate P'(x) = 0, we get 360,000 1 x2 r = 360,000 x= 360,000 = 600 180,000 180,000 : from (ii), y = = 300 600 Thus, for least fencing cost of rectangular pasture dimension's will be 600 inch and 300 inch. Note: (i)you should know Chegg policy. (il) all other questions are based on first question, So please go through this solution.