Q:

Solve the following problems manually or using the MS ExcelMohamed 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

Accepted Solution

A:
Answer:(a) in the step-by-step explanation(b) The optimal solution is 8 chairs and 4 tables.(c) Graph attachedStep-by-step explanation:(a)C: number of small chairsT: number of large tablesMaximize Income = 9T + 3CRestrictions:Wood: 4T+C<=24Glazing: 2T+C<=16In 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=$ 48Point 2 (C=8, T=4)Income = 9*4+3*8 = $ 60 Point 3 (C=0, T=6)Income = 9*6+3*0 = $ 54The optimal solution is 8 chairs and 4 tables.