Question

pierre wants to make some chairs and tables to sell using 360 wooden boards and 1080 nails Each chair uses 6 boards and 12 nails while each table uses 10 boards and 40 nails. Pierre wants to sell no less than 6 tables . IF each chair Sells for $55 and each table sells for $ 125, how many of each should he sell to reach his maximum profit? What will be his maximum profit?

Answer 1

• 30 chairs, 18 tables
• $3900

Explanation:

If x and y represent the numbers of chairs and tables Pierre wants to make, then he wants to ...

Maximize 55x +125y

subject to the constraints ...

6x +10y ≤ 360 . . . . . limit on available boards

12x +40y ≤ 1080 . . . limit on available nails

y ≥ 6 . . . . . . . . . . . . . minimum number of tables to sell

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When there are two variables, it is often convenient to graph the constraints to find the feasible solution region. The graph shows the vertices of the feasible region to be (0, 27), (30, 18), (50, 6), and (0, 6).

Pierre's profit is maximized by selling 30 chairs and 18 tables. His maximum profit is $3900.