DIRECTION:
Show all work â facts, primary and secondary equations, finding the derivatives, doing sign tests, and donât forget to answer the questions asked!
1. A closed box with a square base is to have a volume of 16000 cubic centimeters. The material for the top and bottom of the box costs $3 per square centimeter while the material for the sides costs $1.50 per square centimeter. Find the dimensions of the box that will minimize the total cost of materials. What is the minimum total cost?
2. The management of the UNICO department store has decided to enclose an 800 sq. ft. area outside the building to display potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed on pine boards and the side parallel to the existing external wall of the store will be constructed of galvanized steel fencing material. If the pine board fencing costs $6 per linear foot and the steel fencing costs $3 per linear foot, determine the dimensions of the enclosure that can be constructed at minimum cost. What will the minimum cost be?
DIRECTION:
Show all work â facts, primary and secondary equations, finding the derivatives, doing sign tests, and donât forget to answer the questions asked!
1. A closed box with a square base is to have a volume of 16000 cubic centimeters. The material for the top and bottom of the box costs $3 per square centimeter while the material for the sides costs $1.50 per square centimeter. Find the dimensions of the box that will minimize the total cost of materials. What is the minimum total cost?
2. The management of the UNICO department store has decided to enclose an 800 sq. ft. area outside the building to display potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed on pine boards and the side parallel to the existing external wall of the store will be constructed of galvanized steel fencing material. If the pine board fencing costs $6 per linear foot and the steel fencing costs $3 per linear foot, determine the dimensions of the enclosure that can be constructed at minimum cost. What will the minimum cost be?
