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. Stage ​Children's Standard Executive Cutting 5 hr 4 hr 7 hr Construction 3 hr 2 hr 5 hr Finishing 2 hr 2 hr 4 hr 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 162 hours for​ cutting, 104 hours for​ construction, and 84 hours for finishing. Determine how many of each type of chair the company should make to be operating at full capacity.

Answer 1

Children's model = 7

Standard model = 9

Executive model = 13

Step-by-step explanation:

Let a = number of children's model

b= number of standard model

c = number of executive model

According to the question given, the time allocation is as follows;

Cutting; a = 5 hr b = 4hr c = 7hr, Maximum hours = 162 hours

Construction; a = 3 hr b = 2hr c = 5hr, Maximum hours = 104 hours

Finishing; a = 2 hr b = 2hr c = 4hr, Maximum hours = 84 hours

We can therefore derive the equations.

5a + 4b + 7c = 162 (i)

3a + 2b + 5c = 104 (ii)

2a + 2b + 4c = 84 (iii)

Subtracting (iii) from (ii), a + c = 20, a = 20 - c (iv)

Substituting (iv) into (ii)

60 - 3c + 2b + 5c = 104

2b + 2c = 44 (v)

Substituting (iv) into (i)

100 - 5c + 4b + 7c = 162

4b + 2c = 62 (vi)

Subtracting (v) from (vi), we have

2b = 18; b = 9

Since b + c = 22,

c =22 - 9 = 13

Also, a + c =20

a = 20 - 13 = 7