The following information is used for questions 2830:
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
Final answer
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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