solve 13. d) 13. Choose any 5 of the following problems to complete. Solve the problem by following theprocedure for solving an optimization problem. Show all your steps.A farmer has 1800 m of fencing to make two equal rectangular pens that sharea common side. Determine the dimensions of each pen so that the area is amaximum.New Horizons Travel advertises a package plan for a Florida vacation. The farefor the flight is $400/person plus $8/person for each unsold seat on the plane. Theplane holds 120 passengers and the flight will be cancelled if there are fewer than50 passengers. What number of passengers will maximize revenue?b.c.An open-topped storage box with a square base has a capacity of 5 m. Thematerial for the sides cost $1.60/m?, while the material for the bottom costs $2.00/m?. Find the dimensions that will minimize the cost of making the box.The perimeter of an isosceles triangle is 38 m. Find the length of the sides of thetriangle of maximum area.d.

Answered: The perimeter of an isosceles triangle…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 5SC: If during the following year it is predicted that each comedy skit will generate 30 thousand and...

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If the cost of each Robust tablet increases to 75 c and the cost of each Vigortab increases to 80 c , find the minimum cost.
Solve the following application problem. A rectangular field is to be enclosed by fencing. In addition to the enclosing fence, another fence is to divide the field into two parts, running parallel to two sides. If 1,200 feet of fencing is available, find the maximum area that can be enclosed.
If during the following year it is predicted that each comedy skit will generate 30 thousand and each musical number 20 thousand, find the maximum income for the year. A television program director must schedule comedy skits and musical numbers for prime-time variety shows. Each comedy skit requires 2 hours of rehearsal time, costs 3000, and brings in 20,000 from the shows sponsors. Each musical number requires 1 hour of rehearsal time, costs 6000, and generates 12,000. If 250 hours are available for rehearsal and 600,000 is budgeted for comedy and music, how many segments of each type should be produced to maximize income? Find the maximum income.
Suppose W-Mart is considering purchasing a parcel of land adjacent to the current site on which it plans to build its store. The cost of the parcel is $190,000, and it would enable WMart to increase the size of its store to 160,000 square feet. Discuss whether W-Mart should purchase the land and increase the planned size of the store.
Solve the following maxima and minima problems: A circular cylindrical container, open at the top and having a capacity of 24 cu. In., is to be manufactured. If the cost of the material for the bottom of the container is three times that of the cost of material for the curved part and if there is no waste of material, find the dimensions which will minimize the cost.
Solve the following problems: 1. Find the dimensions of a rectangle with perimeter 1000 meters so that the area of the rectangle is a maximum. 2. A farmer has 8 km of fencing wire and wishes to fence a rectangular piece of land. One boundary of the land is the bank of a straight river. What are the dimensions of the rectangle so that the area is maximized? 3. A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of the sheet is decreasing at a rate of 0.5 m2/sec at what rate is the radius decreasing when the area of the sheet is 12 m2? 4. A tank of water in the shape of a cone is being filled with water at a rate of 12 m3/sec. The base radius of the tank is 26 meters, and the height of the tank is 8 meters. At what rate is the depth of the water in the tank changing when the radius of the top of the water is 10 meters? 5. A cylindrical tank standing upright (with one circular base on the ground) has radius 20 cm. How fast does the water level…
Solve the following maxima and minima problems: A steel storage tank for propane gas is to be constructed in the shape of a right circular cylinder with a hemisphere at both ends. If the desired capacity is 100 cu. ft., What dimensions will require the least amount of steel?
A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular Norman window is to be 20 feet. What should the rectangle's dimensions be in order to maximize the area of the window and, therefore, allow in as much light as possible? The answer to this question is in two parts: first, the width of the rectangle in feet and second, the height of the rectangle in feet.
A financier plans to invest up to $500,000 in two projects. Project A yields a return of 8% on the investment of x dollars, whereas Project B yields a return of 16% on the investment of y dollars. Because the investment in Project B is riskier than the investment in Project A, she has decided that the investment in Project B should not exceed 40% of the total investment. How much should the financier invest in each project in order to maximize the return on her investment? (x, y) = What is the maximum return?

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The perimeter of an isosceles triangle is 38 m. Find the length of the sides of the triangle of maximum area.