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 185 hours for​ cutting, 115 hours for​ construction, and 94 hours for finishing. Determine how many of each type of chair the company should make to be operating at full capacity.

Answer 1

Answer and Explanation:

According to the scenario, computation of the given data are as follow:-

We assume that

X = No. of children

Y  = Standard type

Z = Executive type

So,

5x + 4y + 7z = 185.........(1)

3x + 2y + 5z = 115.........(2)

2x + 2y + 4z = 94

x + y + 2z = 47.........(3)

Equation (2) multiply by 2

6x + 4y + 10z = 230

From equation (1) to (2)

5x + 4y + 7z = 185

6x + 4y + 10z = 230

-x + 0 - 3z = -45

x + 3z = 45.......(4)

Equation (3) multiply by 4

4x + 4y + 8z = 188

From equation (1) to (3)

5x + 4y + 7z = 185

4x + 4y + 8z = 188

x + 0 - z = -3

- x + z = 3……(5)

From equation (5) to (4)

x + 3z = 45

-x + z = 3

4z = 48

Executive type = Z = 48 ÷ 4 = 12

Z = 12 in equation (5)

-x + 12 = 3

x = 9 (children type)

x=9, z=12 in equation 1

5x + 4y + 7z = 185

5 × 9 + 4 × y + 7 × 12=185

45 + 4 × y + 84 = 185

4y = 56 ÷ 4

Y= 14(Standard type)