My Math Forum linear programming problem 2

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 December 16th, 2014, 02:31 PM #1 Newbie   Joined: Dec 2014 From: askard Posts: 9 Thanks: 0 linear programming problem 2 There are 6 pieces of wooden boards of a furniture craftsman and has 28 hours of free time. Sells two types of libraries by the board. Type I library requires 2 wooden boards and 7 hours; The library requires a type II 1 plate and 8 hours. The selling price of 120,000 \$Type I library. The price is 80,000 \$ type II library. According to want to maximize sales revenue Furnishers must be purchased from both models make how many of each? Install problem as a linear programming model. Last edited by greg1313; December 16th, 2014 at 02:34 PM.
 December 17th, 2014, 07:13 PM #2 Global Moderator   Joined: Dec 2006 Posts: 19,982 Thanks: 1853 What does "plate" mean?
December 17th, 2014, 10:18 PM   #3
Math Team

Joined: Dec 2006
From: Lexington, MA

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Hello, kalli1!

Your English is not too accurate.
I'll modify the wording for simplicity.

Quote:
 A furniture craftsman has 6 boards and 28 hours of time. Type A tables require 2 boards and 7 hours of labor. Type B tables require 1 board and 8 hours of labor. Type A tables sell for \$1200; type B tables sell for \$800. How many of each type of table will maximize sales revenue?

Let $x$ = number of type A tables: $\:x \ge 0$
Let $y$ = number of type B tables: $\:y \ge 0$

We have:

$\quad \begin{array}{c|c|c|c|} & \text{boards} & \text{hours} & \text{Revenue} \\ \hline A & 2x & 7x & 1200x \\ B & y & 8y & 800y \\ \hline & 6 & 28 \\ \hline \end{array}$

$\quad\begin{array}{ccc} 2x + y & \le & 6 \\ 7x + 8y &\le & 28 \end{array}$

Then find the coordinates of the vertices of the shaded area.

Then substitute them into the Revenue function: $\:R \;=\;1200x+800y$
$\quad$ and determine which produces maximum revenue.

 December 18th, 2014, 04:36 AM #4 Newbie   Joined: Dec 2014 From: askard Posts: 9 Thanks: 0 sorry for my english and thank you so much.

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