♥♥+LinEAr+PRograming+♥♥

The mini wood market makes a tables and desks. Each table require 10 hours of woodworking and 3 hours of finishing. The desk requires 6 hours of woodworking and 1.5 for finishing. The profit is 145 dir on each table and 75 dir on each desk. There are 60 hours available each week for woodworking and 27 hours for finishing. How many of each item should be produced in order to maximize the profit?
 * Business**

1- Define variables Let t the number of tables produced. Let d the number if desks produced.

2- Write inequalities T ≥0, d ≥0 10t + 6d ≤ 60 3t + 1.5d ≤ 27

3- Graph the system The vertices are (0,0), (0,10), (6,0)



4-write an expression Since profit on each table is 145 dir and the profit on each desk is 75 dir, the profit function is P(t,d)= 145t + 75d

4- Substitute values P(0,0)= 145(0) + 75(0)=0 P(0,10)=145(0) + 75(10)= 750 P(6,0)=145(6) + 75(0)= 870

5- the problem has alternate optional solutions. The market will maximize the profit if they made 6 tables…

♥♥ H.O.T♥♥ Japan used linear programming to aid the farmers choices of crops and other forms of agricultural production. This led to a 20% increase in crop profits, a 62% increase in animal husbandry profits, while improving the region’s ecology. Suppose a Japanese farmer has 86 miles on which to grow mango and orange. He is planting at least 12 miles of mango and 16 miles of orange. Based on his calculations, he can earn 155 dir per mile of mango and 200 dir per mile of orange. If the farmer plants at least 2 miles of mango for every mile of orange, how many miles of each should he plant to earn the greatest profit? And what is the farmer maximum profit?
 * Agriculture**

Other solved question...

The manger of a falafel restaurant is selling falafel sandwiches and Falafel plates. each falafel sandwich costs 2$, and each Falafel plate costs 5$. each falafel sandwich need to have 4 pieces of falafel, and each falafel plate need to have 10 pieces of flafel. the owner wants to use a no more than 1000 falafel, and the manger need at least 100 falafel sandwich and 50 Falafel plate. how many of each they should make to minimize the cost?

plate sandwich total

10x 4y < or equal to 1000 x > 50 y > 100

table for 10x+4y=1000

0 250 10 0

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