Chapter 8.4, Problem 85AE

Computing the Cost of Production The Acme Steel Company is a producer of stainless steel and aluminum containers. On a certain day, the following stainless steel containers were manufactured: 500 with 10-gallon (gal) capacity, 350 with 5-gal capacity, and 400 with 1-gal capacity. On the same day, the following aluminum containers were manufactured: 700 with 10-gal capacity,500 with 5-gal capacity, and 850 with 1-gal capacity.

a. Find a 2 by 3 matrix representing these data. Find a3 by 2 matrix to represent the same data.

b. If the amount of material used in the 10-gal containers is 15 pounds (lb), the amount used in the 5-gal containers is 8 lb, and the amount used in the 1-gal containers is 3 lb, find a 3 by 1 matrix representing the amount of material used.

c. Multiply the 2 by 3 matrix found in part (a) and the 3 by 1 matrix found in part (b) to get a 2 by 1 matrix showing the day’s usage of material.

d. If stainless steel costs Acme $\$0.10$ per pound and aluminum costs $\$0.05$ per pound, find a 1 by 2 matrix representing cost.

e. Multiply the matrices found in parts (c) and (d) to determine the total cost of the day’s production.