The Donaldson Furniture Company produces three types of rock

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 199 hours for cutting, 123 hours for construction, and 98 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

Solution

Sol)

Let X1 be the number of chairs

Let X2 be the standard chairs

Let X3 be the children\'s chairs

Problem is

Entering =X1, Departing =S1, Key Element = 5

R1 (new) =R1 (old) ÷5=R1 (old) 15

R2 (new) =R2 (old) 3R1 (new)

R3 (new) =R3 (old) 2R1 (new)

Entering =X2, Departing =S3, Key Element = 25

R3 (new) =R3 (old) ÷25=R3 (old) 52

R1 (new) =R1 (old) 45R3 (new)

R2(new) =R2 (old) +25R3(new)

Since all CjZj0,

Optimum Solution is arrived with value of variables as :
X1=3

X2=46

X3=0

Maximise Z=49

Hence

X1 be the number of chairs=3

X2 be the standard chairs=46

X3 be the children\'s chairs=0

MAX Z= 1 X1+ 1 X2+ 1 X3

Subject to constraints

5 X1+ 4 X2+ 7 X3 199 3 X1+ 2 X2+ 5 X3 123 2 X1+ 2 X2+ 4 X3 98

and X1,X2,X30