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 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)

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