Suppose that you own a company that produces cans of soup. A 10 ¾ ounce can of soup is to

contain 12 cubic inches of soup. The cost of materials for the top and bottom of the can is 5

cents per square inch, and the cost of the materials for the side of the can is 3 cents per square

inch. To minimize cost, what should the dimensions of the can be?

1. Solve the problem to determine the proper dimensions to minimize the cost of

manufacturing each can. What is the minimum cost of the material? (3 points)

2. Suppose that the ingredients of the soup costs $.95 for each can of soup that is

produced, and the minimum cost of the materials to make each can is the amount you

derived in part 1 above, and when the fixed cost is factored in (the factory, employee

salaries, management salaries, utilities, etc.), the fixed cost is $1500 per day. Also,

suppose that you sell each can of soup for $3.79. Determine the (a) overall cost

function of producing the cans each day, (b) the revenue function, and (c) the profit

function. How many cans does your company need to produce each day to start making

a profit?