A Manufacturer Has the Capability to Produce Both Chairs and Tables

question 71

Multiple Choice

A manufacturer has the capability to produce both chairs and tables. Both products use the same materials (wood, nails and paint) and both have a setup cost ($100 for chairs, $200 for tables) . The firm earns a profit of $20 per chair and $65 per table and can sell as many of each as it can produce. The daily supply of wood, nails and paint is limited. To manage the decision-making process, an analyst has formulated the following linear programming model:
Max 20x1 + 65x2 - 100y1 - 200y2
s.t. 5x1 + 10x2 ? 100 {Constraint 1}
20x1 + 50x2 ? 250 {Constraint 2}
1x1 + 1.5x2 ? 10 {Constraint 3}
My1 ? x1 {Constraint 4}
My2 ? x2 {Constraint 5} $$y _ { i } = \left\{ \begin{array} { l } 1 , \text { if product } j \text { is produced } \\0 , \text { otherwise }\end{array} \right.$$
Which of the constraints limit the amount of raw materials that can be consumed?

• A) Constraint 1
• B) Constraint 4
• C) Constraint 5
• D) Constraint 1 and 4 only
• E) None of these

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Definitions:

Numerals

Symbols or characters used to represent numbers.

Adding

The mathematical process of combining two or more quantities to get a total or sum.

Borrowing

The act of receiving something from someone with the intention of returning it or its equivalent later.

Decimals

Numerical symbols used in the decimal system, involving a point that separates the whole number from the fractional part.