Question

17-1 A lidless, rectangular box is to be manufac- tured from 30- by 40-inch cardboard stock sheets by cutting squares from the four corners, folding siz 17- pro eve up ends and sides, and joining with heavy tape. The designer wishes to choose box dimensions the set that maximize volume. est (a) Formulate this design problem as a con- strained NLP. (b) Use class optimization software to start from a feasible solution and compute at least a local optimum

Answer 1

Let the required box has l,b,h as the dimension and thus the volume of the box is l*b*h, which is to be maximized. Given that the dimensions of the sheet are 30 x 40 inch. Thus the constrained should be framed such that the sum of the length side of the box and the respective length cut out is 40 and similarly the breadth and its cut out must be 30 inch. And the sum of areas of all sides and the squares cut out must be equal to the area of the sheet which is 30*40=1200.sq-inch. This can be written as,

Maximize,

l*b*h

Subject to constraints,

l+2h=40;

b+2h=30;

2lh+2bh+lb+4h² = 1200

l,b,h $\geq$ 0;