Question

Solve the following problems manually or using the MS Excel

Mohamed has enough wood to make 24 small chairs or 6 large tables. In other words, the large tables require 4 times the amount of wood as the small chairs. He only has enough of a special glazing compound to glaze 16 of the small chairs or 8 of the large tables. Let X1 the number of small chairs and X2 the number of large tables. The smaller chairs sell for $3 each, while the larger tables would bring $9 each.

(a) Formulate the Problem.

(b) Solve the Linear Programming Problem.

(c) Solve also graphically

Answer 1

(a) in the step-by-step explanation

(b) The optimal solution is 8 chairs and 4 tables.

(c) Graph attached

Explanation:

(a)

C: number of small chairs

T: number of large tables

Maximize Income = 9T + 3C

Restrictions:

Wood: 4T+C<=24

Glazing: 2T+C<=16

In the graph its painted in green the "feasible region" where lies every solutions that fit the restrictions.

One of the three points marked in the graph is the optimal solution.

Point 1 (C= 16, T= 0)

Income = 9*0+3*16=$ 48

Point 2 (C=8, T=4)

Income = 9*4+3*8 = $ 60

Point 3 (C=0, T=6)

Income = 9*6+3*0 = $ 54

The optimal solution is 8 chairs and 4 tables.