1. The cost per unit produced at a certain facility is represented by the function

UC = 2x^2 - 10x + 50

2. The cost of producing and selling a certain item is for the first 1,000 units, for a production range between 1,000 and 2,500 units, and 2,500 units, $205x - $97,500 where for more than 2,500 units, 205x - $97,500where x is the number of units produced. If the selling price is $200 per unit, and all units produced are sold, find the level of production that will maximize profit

3. It has been found that the heat loss through the ceiling of a building is 0.13 Btu per hour per square foot of area for each 1F of temperature difference. If the 2,200 feet2 ceiling is insulated, the heat loss in Btu per hour per degree temperature difference per square foot of area is taken as

1/((1/0.13) +(t/0.27))

4. As an alternative to the used automobile in Problem 10, the student can purchase a new utility model for $13,600 with a 3-year warranty. First-year maintenance cost is expected to be $50, and the maintenance cost will increase by $50 per year thereafter. Operation costs for this new automobile are expected to be $960 for each year of use and its salvage value decreases by 20% per year. What is the economic advantage of the new automobile without interest; with interest at 10%? .

5. An engine remanufacturer requires 82 pistons per day in its assembly operations. No shortages are to be allowed. The machine shop can produce 500 pistons per day. The cost associated with initiating manufacturing action is $400 and the holding cost is $0.45 per piston per day. The manufacturing cost is $105 per piston. (a) Find the minimum-cost production quantity. (b) Find the minimum-cost procurement level if production lead time is 8 days. (c) Calculate the total system cost per day