# Formulating Linear Programming Model

1. A company produces two products that are processed on two assembly lines. Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours. Each product requires 10 hours of processing time on line1, while on line 2 product 1 requires 7 hours and product 2 requires 3 hours. The profit for product 1 is $6 per unit, and the profit for product 2 is $4 per unit.

a. Formulate a linear programming model for this problem.

2. The Pinewood Furniture Company produces chairs and tables for two resources-labor and wood. The company has 80 hours of labor and 36 board-ft. of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 board-ft. of wood, whereas a table requires 10 hours of labor and 6 board-ft. woo. The profit derived from each chair is $400 and from each table, $100. The company wants to determine the number of chairs and tables to produce each day in order to maximize profit.

a. Formulate a linear programming model for this problem.

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#### Solution Preview

1. A company produces two products that are processed on two assembly lines. Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours. Each product requires 10 hours of processing time on line1, while on line 2 product 1 requires 7 hours and product 2 requires 3 hours. The profit for product 1 is $6 per unit, and the profit for product 2 is $4 per unit.

a. Formulate a linear programming model for this problem.

Let x denotes units of product1 and y denotes units of ...

#### Solution Summary

There are two problems. Solution to each problem explains the steps to formulate a linear programming model.