A balloon carrying an x-ray telescope and other scientific equipment must be designed and launched. A rough measure of performance can be expressed in terms of the height reached by the balloon and the weight of the equipment lifted. Clearly, the height itself is a function of the balloon’s volume.
The project to be undertaken has a budget constraint of $1040. The cost associated with the volume V is 2V, and the cost of the equipment is 4W. In order to ensure that a reasonable balance is obtained between performance due to the height and that due to the scientific equipment, the designer has to meet the constraint 80W ≥ 100V.
Find the optimal design in terms of volume and equipment weight, solving by the Frank-Wolfe algorithm.