1.(a) You have been asked to bid on the construction of a square-bottomed box with no top which will hold 100 cubic inches of water. If the bottom and sides are made from the same material, what are the dimensions of the box which uses the least material? (Assume that no material is wasted.)

(b) Suppose the box in part (a) uses different materials for the bottom and the sides. If the bottom material costs 5 per square inch and the side material costs 3 per square inch, what are the dimensions of the least expensive box which will hold 100 cubic inches of water?

2. In the planning of a coffee shop, we estimate that if there is seating for between 40 and 80 people, the daily profit will be $50 per seat. However, if the seating capacity is more than 80 places, the daily profit per seat will be decreased by $1 for each additional seat over 80. What should the seating capacity be in order to maximize the coffee shop's total profit?

3.The total cost in dollars for Alicia to make q oven mitts is given by C(q)= 64 +1.5q+0.1q^2 .

(a) What is the fixed cost? (b) Find a function that gives the marginal cost. (c) Find a function that gives the average cost. (d) Find the quantity that minimizes the average cost. (e) Confirm that the average cost and marginal cost are equal at your answer to part (d).