The Donaldson Furniture Company produces three types of rocking chairs: the chil

Question

The Donaldson Furniture Company produces three types of rocking chairs: the children's model, the standard model, and the executive model. Each chair is made in three stages: cutting, construction and finishing. The time needed for each stage of each chair is given in the chart. During a specific week the company has available a maximum of 156 hours for cutting. 94 hours for construction, and 76 hours for finishing. Determine how many of each type of chair the company should make to be operating at full capacity. The number of executive chairs the company should make is The number of standard chairs the company should make is The number of children's chairs the company should make is

Explanation / Answer

Solution:

Children's - x chairs
Standard - y chairs
Executive - z chairs

here given cutting time is = 156 hrs

so, 5x+4y+7z = 156 -------> eq 1
3x+2y+5z = 94 ---------> eq 2
2x+2y+4z = 76 ---------> eq 3
from eq 1 and 2 :
2x+2y+2z = 62
s0, x+y+z = 31 ------>eq 4
from eq 2 and 3
x+z = 18 --------> eq 5
from eq 4 nd 5
S0, y = 13

3x+2y+5z = 94
3x+ 5z = 68
x+z = 18
solve above equations by substitution
3(18-z) + 5z = 68
54-3z + 5z = 68
2z = 14
z = 7

and thus, x+z = 18 => x = 11
So, the answer is:

The number of executive chairs the company should make is 7
The number of standard chairs the company should make is 13
The number of children's chairs the company should make is 11

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