1
Optimization Problems- HW Problems
1. A cylindrical metal container without a top is to be made with a
volume of 100𝑓𝑡 3 . Find the dimensions that will minimize the cost of
the metal to manufacture it.
2. Find two positive numbers so that the second number is the
reciprocal of the first number and the sum of the two numbers is a
minimum.
3. A rectangular box with a square base is to be made with two
materials. The material for the top and four sides costs $4/𝑓𝑡 2 and the
material for the bottom costs $8/𝑓𝑡 2 . Find the dimensions of the box
with greatest possible volume if you can spend $1,152.
4. Find the area of the largest rectangle that has its vertices in the first
and second quadrant on the parabola 𝑦 = 9 − 𝑥 2 and one side along
the 𝑥-axis.
5. Ten feet of wire is used to form a circle and a square. How much of
the wire should be used for each figure to maximize the enclosed area?
6. Find the closest point of the line 𝑦 = 2𝑥 + 5 to (0,0).
Optimization Problems- HW Problems
1. A cylindrical metal container without a top is to be made with a
volume of 100𝑓𝑡 3 . Find the dimensions that will minimize the cost of
the metal to manufacture it.
2. Find two positive numbers so that the second number is the
reciprocal of the first number and the sum of the two numbers is a
minimum.
3. A rectangular box with a square base is to be made with two
materials. The material for the top and four sides costs $4/𝑓𝑡 2 and the
material for the bottom costs $8/𝑓𝑡 2 . Find the dimensions of the box
with greatest possible volume if you can spend $1,152.
4. Find the area of the largest rectangle that has its vertices in the first
and second quadrant on the parabola 𝑦 = 9 − 𝑥 2 and one side along
the 𝑥-axis.
5. Ten feet of wire is used to form a circle and a square. How much of
the wire should be used for each figure to maximize the enclosed area?
6. Find the closest point of the line 𝑦 = 2𝑥 + 5 to (0,0).
