Question

# The following information is used for questions 28-30: The Hickory Cabinet & Furniture Company produces sofas,...

The following information is used for questions 28-30:

The Hickory Cabinet & Furniture Company produces sofas, tables and chairs.  The plant uses three main resources to make furniture:  wood, upholstery and labor.  The unit profits, the resource requirements for each piece of furniture and the total resources available weekly are as follows:

 Profit/unit Wood (lb) Upholstery (yd) Labor (hour) Sofa \$400 7 12 6 Table 275 5 -- 9 Chair 190 4 7 5 Total available resources: 2250 1750 2000

The furniture is produced on a weekly basis and stored in a warehouse until the end of the week, when it is shipped out.  The warehouse has a total capacity of 650 pieces of furniture.  Let x1 be the number of sofas produced, x2 be the number of tables produced and x3 be the number of chairs produced.  An LP model is set up and solved as follows:

Maximize Z = 400x1 + 275x2 + 190x3

Subject to:

(Constraint 1)    7x1 + 5x2 + 4x3 ≤ 2250 lb

(Constraint 2)    12x1 + 7x3 ≤ 1750 yd

(Constraint 3)    6x1 + 9x2 + 5x3 ≤ 2000 hr

(Constraint 4)    x1 + x2 + x3 ≤ 650 pieces

x1, x2, x3 ³0

28.  How many sofas, tables and chairs will the company produce?

A.) 146 sofas, 0 tables, 125 chairs

B.) 125 sofas, 0 tables, 146 chairs

C.) 0 sofas, 146 tables, 125 chairs

D.)146 sofas, 125 tables, 0 chairs

E.)125 sofas, 146 tables, 0 chairs

The following linear programming problem can be solved in Excel using the information and definitions that have been provided above.

X1 = number of sofas produced

X2 = number of tables produced

X3 = number of chairs produced

Objective function

Maximize Z = 400x1 + 275x2 + 190x3

Constraints

7x1 + 5x2 + 4x3 ≤ 2250 lb

12x1 + 7x3 ≤ 1750 yd

6x1 + 9x2 + 5x3 ≤ 2000 hr

x1 + x2 + x3 ≤ 650 pieces

x1, x2, x3 >= 0

The first step is the formulation of the table

Formulas used

Solver inputs

From the final answer, we can see that the Hickory Cabinet & Furniture Company should produce 146 sofas, 125 tables, and 0 chairs.

Hence the correct answer is option D.

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