1. You are on a tight budget and are planning to take a trip that is X miles away. Develop a model that determines your round-trip gasoline costs. What assumptions or approximations are necessary to treat this model as a deterministic model? Are these assumptions or approximations acceptable to you?

1. The Sun Blazer sunglass company will produce a 50^th anniversary edition of the first pair ever produced if the order size is large enough to provide a profit. For each special style order the company incurs a fixed cost of $2,500 for production set-up. The variable cost is $50 per pair, and they will sell for $90.
2. Let x indicate the number of sunglasses produced. Develop a mathematical model for total profit realized from an order of X pair of glasses.
3. Let P indicate the profit. Develop a mathematical model for the total profit realized from an order of a pair of sunglasses.
4. How large must the order for sunglasses be before Sun Blazer will break even?

1. The Johnson Ladder Manufacturing company is located in Johnson City TN. The company assembles fiberglass stepladders and receives plastic tops from two sources. One source is located in Detroit MI and the other in Louisville KY. Let x = the number of products received from Detroit and y = the number of units received from Louisville.
   1. Give an expression for the total number of units received by the plant in Johnson City.
   2. Shipments from Detroit cost $0.30 per unit and shipments from Louisville cost $0.35. Develop an objective function representing the total cost of shipments to Johnson City.
   3. Assuming that the monthly demand for tops in 6,000 units, develop a constraint that requires 6,000 to be shipped to Johnson City.
   4. No more than 3,500 units can be shipped from Detroit and 4,000 can be shipped from Louisville in a month. Develop constraints to model the situation.
   5. Negative amounts cannot be shipped. Combine the objective function and constraints and develop a mathematical model for satisfying the demand at Johnson City at minimum cost.