Answer to Question #247862 in Economics for xyz

Question

The Pinewood Furniture Company produces chairs and tables from two resources: labor and wood.

The company has 145 hours of labor and 100 board-ft. of wood available each day. Demand for tables is limited to 8 per day.  Each chair requires 3 hours of labor and 4 board-ft. of wood, whereas a table requires 22 hours of labor and 9 board-ft. of wood. The profit derived from each chair is $100 and from each table is $500. The company wants to determine the number of chairs and tables to produce each day in order to maximize profit.

The correct linear programming model formulation of this problem is:

Answer 1

$$f=100x+500y \to max$$

$$3x+22y\le 145$$

$$4x+9y\le100$$

$$x\ge 0$$

$$y\ge0$$

$$x=14$$

$$y=5$$

$$Profit=3900$$