SOLUTION: A division of the Winston Furniture Company manufactures dining tables and chairs. Each table requires 40 board feet of wood and 6 labor-hours. Each chair requires 16 board feet of

Question 1201321: A division of the Winston Furniture Company manufactures dining tables and chairs. Each table requires 40 board feet of wood and 6 labor-hours. Each chair requires 16 board feet of wood and 4 labor-hours. The profit for each table is $45, and the profit for each chair is $25. In a certain week, the company has 3200 board feet of wood available and 520 labor-hours available. How many tables and chairs should Winston manufacture to maximize its profit?
tables: ?
chairs: ?
What is the maximum profit?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = number of dining tables.
y = number of chairs.
constraints:
40x + 16y <= 3200
6x + 4y <= 520
x >= 0
y >= 0
objective function:
maximize 45x + 25y
graph oppositve of constraints.
unshaded area is region of feasibility.
evaluate objective function at corner points of feasible region.
find coordinate points where profit is maximum.
that's your solution.
maximum profit is at (70,25) = 70 * 45 + 25 * 25 = 3775
that's 70 tables and 25 chairs.
constraints are satisfied because:
70 * 40 + 25 * 16 = 3200 which is <= 3200
70 * 6 + 25 * 4 = 520 which is <= 520
here's the graph.

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