Using a note taking program (for example OneNote) or manually on a piece of paper

, plot all the constraints

(using the intercept values) and shade the appropriate side of each constraint. Identify the feasible region as the

polygon formed by the intersection of all shaded regions. Name the corners of the feasible region with letters (A,

B, C, etc.). Arbitrarily select one of these corners and assume that the objective line passes through it. Plug in the

coordinates of this point to find the corresponding objective line formula. then find a second on this objective

line preferably on an axis to draw the objective line. Move the objective line to advance the objective function

value as far as possible (without changing its slope) to find the optimal solution and draw the the objective line

passing through the optimal solution. Find the coordinates of the optimal solution by solving the system of the

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equations that belong to the constraint lines that pass through this optimal solution. Show all your work in detail

and make sure that your graphical solution is legible and well drawn as this will af

fect the credit you will earn

for this question.

The Pinewood Furniture Company produces chairs and tables from 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. of wood. 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. Solve this model by using linear programming.