Question

[15pts) A lidless cardboard box with a volume 10m e material for the bottom of the box costs 5 oat and the materia dolla2. Find the dimensions of the box that es of the imize the cost of the box. mize the cost or do Draw the picture and identify the variables. entify the objective function. Write it in terms of the variables of the method of Lagrage multipliers to find the dimensions of the box that cost of the box

Answer 1

4 Given hal volume - o tteu volume=xyz Then and cost or botton5 dollas : Total cost for botloin5y Το ial cos, tor malong-He whole hox-@r③ eeune ohjetve fandhen

Lagange numbe 5y 5 29 27-2ス 0Z

2 52

substitute y z-1 1/