Ch4, Problem 14: Part a - LP Formulation

Write down the formulation in the answer box below.

Make sure the following four components are included:

1. Variable definitions:

• Use a separate line for variable;
• Start each variable definition with "Let";
• Example: Let x1 denote ...
• Specify the units.
• Example: number of bags, gallons of a liquid, pounds (lbs) of flours, etc.

1. An objective function:

• Start with either "max Z=" or "min Z=";
• Include only linear terms of decision variables after ``=".

1. A set of constraints:

• Start with "s.t." for the 1st constraint;
• Left-hand-side (LHS) of each constraint should only include linear terms of decision variables;
• Right-hand-side (RHS) of each constraint should only have numbers;
• Do not include ``s.t." for other constraints.

1. A set of variable restrictions:

• Start with "and";
• Group variable restrictions if they are allnon-negatively restricted.

Suggestion: you may find it easier to use the Table editor () so that the objective function, each constraint, and the variable restrictions are in their separate lines.

Ch4, Problem 14, Part b - Solving LP

• In an Excel file, set up the model and find the solution using Solver.
• In the same Excel file, develop the table that will show for each quarter the number of units to manufacture, the ending inventory, and the costs incurred.
• Under Resources - Excel Solveron theHomepage, you can find examples of how to set up a LP model in Excel and solve it using Solver.
• Upload a single Excel file.

14. The production manager for the Classic Boat Corporation must determine how many units of the Classic 21 model to produce over the next four quarters. The company has a beginning inventory of 100 Classic 21 boats, and demand for the four quar- ters is 2000 units in quarter 1, 4000 units in quarter 2, 3000 units in quarter 3, and 1500 units in quarter 4. The firm has limited production capacity in each quarter. That is, up to 4000 units can be produced in quarter 1, 3000 units in quarter 2, 2000 units in quarter 3, and 4000 units in quarter 4. Each boat held in inventory in quarters 1 and 2 incurs an inventory holding cost of $250 per unit; the holding cost for quarters 3 and 4 is $300 per unit. The production costs for the first quarter are $10,000 per unit; these costs are expected to increase by 10% each quarter because of increases in labor and material costs. Management specified that the ending inventory for quarter 4 must be at least 500 boats.a. Formulate a linear programming model that can be used to determine the production schedule that will minimize the total cost of meeting demand in each quarter subject to the production capacities in each quarter and also to the required ending inventory in quarter 4. b. Solve the linear program formulated in part (a). Then develop a table that will show for each quarter the number of units to manufacture, the ending inventory, and the costs incurred