Optimum Design
183
3.22. Taylor A. Advanced Calculus, Ginn and Co, 1955.
3.23. Vidosic JP. (1969) Elements of Design Engineering, New York: The Ronald
Press Co, 1969.
3.24. Wahl AM. Variable Stresses in Springs, January-April 1938 Machine Design,
Penton Co., Cleveland.
3.25. Wilde D J, Beightler CS, Foundations of Optimization, Englewood Cliffs, N J:
Prentice-Hall, 1967. Also a later 2nd ed.
3.26. Yasak T. A method of minimum weight design with requirements imposed on
stresses and natural frequencies, Report 452, Institute of Space and Aeronautical Science, Uaiversity of Tokyo, 1970.
PROBLEMS
PROBLEM 3.1
Find the dimensions of the largest area rectangle that can be inscribed in a
circle with a radius of 10 ft.
PROBLEM 3.2
Storage containers are to be produced having a volume of 100 cubic feet
each. They are to have a square base and an open top. What dimensions
should the container have in order to minimize the amount of material
required (i.e. minimize the cost)?
PROBLEM 3.3
A manufacturer produces brass bolts and mild steel bolts at an average cost
of 40¢ and 20¢, respectively. If the brass bolts are sold for X cents and the
mild steel bolts are sold for Ycents, the market per quarter is 4,000,O00/XY
brass bolts and 8,000,O00/XY mild steel bolts. Find the selling prices for
maximum profit.
PROBLEM 3.4
A thin wall cantilever tube with a thickness t greater than 0.002 in and 60 in
long is loaded at the tip with a 500 lbs load offset 6 in. perpendicular from
the center of the tube. The material is 6061-T6 aluminum with an allowable
tension of 31,900 psi. Include the torsional buckling and bending perpendicular buckling constraints. Solve for the minimum weight of the tube using
nonlinear or geometric programming.
183
3.22. Taylor A. Advanced Calculus, Ginn and Co, 1955.
3.23. Vidosic JP. (1969) Elements of Design Engineering, New York: The Ronald
Press Co, 1969.
3.24. Wahl AM. Variable Stresses in Springs, January-April 1938 Machine Design,
Penton Co., Cleveland.
3.25. Wilde D J, Beightler CS, Foundations of Optimization, Englewood Cliffs, N J:
Prentice-Hall, 1967. Also a later 2nd ed.
3.26. Yasak T. A method of minimum weight design with requirements imposed on
stresses and natural frequencies, Report 452, Institute of Space and Aeronautical Science, Uaiversity of Tokyo, 1970.
PROBLEMS
PROBLEM 3.1
Find the dimensions of the largest area rectangle that can be inscribed in a
circle with a radius of 10 ft.
PROBLEM 3.2
Storage containers are to be produced having a volume of 100 cubic feet
each. They are to have a square base and an open top. What dimensions
should the container have in order to minimize the amount of material
required (i.e. minimize the cost)?
PROBLEM 3.3
A manufacturer produces brass bolts and mild steel bolts at an average cost
of 40¢ and 20¢, respectively. If the brass bolts are sold for X cents and the
mild steel bolts are sold for Ycents, the market per quarter is 4,000,O00/XY
brass bolts and 8,000,O00/XY mild steel bolts. Find the selling prices for
maximum profit.
PROBLEM 3.4
A thin wall cantilever tube with a thickness t greater than 0.002 in and 60 in
long is loaded at the tip with a 500 lbs load offset 6 in. perpendicular from
the center of the tube. The material is 6061-T6 aluminum with an allowable
tension of 31,900 psi. Include the torsional buckling and bending perpendicular buckling constraints. Solve for the minimum weight of the tube using
nonlinear or geometric programming.