do all Excercise 2.5 Q15,Q19&Q21q23 needed Please solve all questions in the order to get positive feedback These are easy questions you must have to solve all please By Hans solution needed only 15. Cost A rectangular garden of area 75 square feet is to be sur-rounded on three sides by a brick wall costing S10 per footand on one side by a fence costing $5 per foot. Find thedimensions of the garden that minimize the cost of materials.16. Cost A closed rectangular box with a square base and a vol-ume of 12 cubic feet is to be constructed from two differenttypes of materials. The top is made of a metal costing $2 persquare foot and the remainder of wood costing S1 per squarefoot. Find the dimensions of the box for which the cost ofmaterials is minimized.17. Surface Area Find the dimensions of the closed rectangularbox with square base and volume 8000 cubic centimeters thatcan be constructed with the least amount of material.18. Volume A canvas wind shelter for the beach has a back, twosquare sides, and a top. Find the dimensions for which thevolume will be 250 cubic feet and that requires the least pos-sible amount of canvas.19. Area A farmer has $1500 available to build an E-shaped fencealong a straight river so as to create two identical rectangu-lar pastures. (See Fig. 13.) The materials for the side parallelto the river cost $6 per foot, and the materials for the threesections perpendicular to the river cost $5 per foot. Find thedimensions for which the total area is as large as possible.Figure 13 Rectangularpastures along a river.20. Area Find the dimensions of the rectangular garden of great-est area that can be fenced off (all four sides) with 300 metersof fencing.21. Maximizing a Product Find two positive numbers, x and y,whose sum is 100 and whose product is as large as possible.22. Minimizing a Sum Find two positive numbers, x and y, whoseproduct is 100 and whose sum is as small as possible.23. Area Figure 14(a) shows a Norman window, which consistsof a rectangle capped by a semicircular region. Find the valueof x such that the perimeter of the window will be 14 feet andthe area of the window will be as large as possible.2π.χadresRiver2x(a)hh(b)Side unrolledhFigure 14maldor24. Surface Area A large soup can is to be designed so that thecan will hold 167 cubic inches (about 28 ounces) of soup. [SeeFig. 14(b).] Find the values of x and h for which the amountof metal needed is as small as possible.25. In Example 3 we can solve the constraint equation (2) for x insteadof w to get x = 20-w. Substituting this for x in (1), we getA = xw = 20 --ww.- 1/2ww.2.5 Optimization Problems 169Sketch the graph of the equationA = 20wand show that the maximum occurs when w= 20 and x 10.26. Cost A ship uses 5x² dollars of fuel per hour when traveling ata speed of x miles per hour. The other expenses of operatingthe ship amount to $2000 per hour. What speed minimizes thecost of a 500-mile trip? [Hint: Express cost in terms of speedand time. The constraint equation is distance speed x time.]27. Cost A cable is to be installed from one corner, C, of a rectan-gular factory to a machine, M, on the floor. The cable will runalong one edge of the floor from C to a point, P, at a cost of$6 per meter, and then from P to M in a straight line buriedunder the floor at a cost of $10 per meter (see Fig. 15). Let xdenote the distance from C to P. If M is 24 meters from thenearest point, A, on the edge of the floor on which lies, andA is 20 meters from C, find the value of x that minimizes thecost of installing the cable and determine the minimum cost.20xFigure 16PyFigure 1528. Area A rectangular page is to contain 50 square inches of print.The page has to have a 1-inch margin on top and at the bottomand a -inch margin on each side (see Fig. 16). Find the dimen-sions of the page that minimize the amount of paper used.in.in.24Print Area Prist Area Print AreaPrint Area Print Area Print AreaPrist Aren Print Area Print AreaPrint Area Print Aren PrintPrint AreaM1 in.1 in.

Question

do all Excercise 2.5  Q15,Q19&Q21q23 needed Please solve all questions in the order to get positive feedback These are easy questions you must have to solve all please  By Hans solution needed only 15. Cost A rectangular garden of area 75 square feet is to be sur-rounded on three sides by a brick wall costing S10 per footand on one side by a fence costing $5 per foot. Find thedimensions of the garden that minimize the cost of materials.16. Cost A closed rectangular box with a square base and a vol-ume of 12 cubic feet is to be constructed from two differenttypes of materials. The top is made of a metal costing $2 persquare foot and the remainder of wood costing S1 per squarefoot. Find the dimensions of the box for which the cost ofmaterials is minimized.17. Surface Area Find the dimensions of the closed rectangularbox with square base and volume 8000 cubic centimeters thatcan be constructed with the least amount of material.18. Volume A canvas wind shelter for the beach has a back, twosquare sides, and a top. Find the dimensions for which thevolume will be 250 cubic feet and that requires the least pos-sible amount of canvas.19. Area A farmer has $1500 available to build an E-shaped fencealong a straight river so as to create two identical rectangu-lar pastures. (See Fig. 13.) The materials for the side parallelto the river cost $6 per foot, and the materials for the threesections perpendicular to the river cost $5 per foot. Find thedimensions for which the total area is as large as possible.Figure 13 Rectangularpastures along a river.20. Area Find the dimensions of the rectangular garden of great-est area that can be fenced off (all four sides) with 300 metersof fencing.21. Maximizing a Product Find two positive numbers, x and y,whose sum is 100 and whose product is as large as possible.22. Minimizing a Sum Find two positive numbers, x and y, whoseproduct is 100 and whose sum is as small as possible.23. Area Figure 14(a) shows a Norman window, which consistsof a rectangle capped by a semicircular region. Find the valueof x such that the perimeter of the window will be 14 feet andthe area of the window will be as large as possible.2π.χadresRiver2x(a)hh(b)Side unrolledhFigure 14maldor24. Surface Area A large soup can is to be designed so that thecan will hold 167 cubic inches (about 28 ounces) of soup. [SeeFig. 14(b).] Find the values of x and h for which the amountof metal needed is as small as possible.25. In Example 3 we can solve the constraint equation (2) for x insteadof w to get x = 20-w. Substituting this for x in (1), we getA = xw = 20 --ww.- 1/2ww.2.5 Optimization Problems 169Sketch the graph of the equationA = 20wand show that the maximum occurs when w= 20 and x 10.26. Cost A ship uses 5x² dollars of fuel per hour when traveling ata speed of x miles per hour. The other expenses of operatingthe ship amount to $2000 per hour. What speed minimizes thecost of a 500-mile trip? [Hint: Express cost in terms of speedand time. The constraint equation is distance speed x time.]27. Cost A cable is to be installed from one corner, C, of a rectan-gular factory to a machine, M, on the floor. The cable will runalong one edge of the floor from C to a point, P, at a cost of$6 per meter, and then from P to M in a straight line buriedunder the floor at a cost of $10 per meter (see Fig. 15). Let xdenote the distance from C to P. If M is 24 meters from thenearest point, A, on the edge of the floor on which lies, andA is 20 meters from C, find the value of x that minimizes thecost of installing the cable and determine the minimum cost.20xFigure 16PyFigure 1528. Area A rectangular page is to contain 50 square inches of print.The page has to have a 1-inch margin on top and at the bottomand a -inch margin on each side (see Fig. 16). Find the dimen-sions of the page that minimize the amount of paper used.in.in.24Print Area Prist Area Print AreaPrint Area Print Area Print AreaPrist Aren Print Area Print AreaPrint Area Print Aren PrintPrint AreaM1 in.1 in.

Accepted Answer

As per the guidelines, I am providing the solution to the first question.
Given the area of a…

15. Cost A rectangular garden of area 75 square feet is to be sur- rounded on three sides by a brick wall costing $10 per foot and on one side by a fence costing $5 per foot. Find the dimensions of the garden that minimize the cost of materials.