Question

Two types of widgets, namely type A and type B, are produced on a machine. The number of machine hours available per week is 80. How many widgets of type A must be produced? I. One unit of type A widget requires 2 machine hours and one unit of type B widget requires 4 machine hours.
I II. The widget dealer wants supply of at least 10 units of type A widget per week and he would not accept less than 15 units of type B widget.

• A. If the question can be answered with the help of statement I alone
• B. If the question can be answered with the help of statement II alone
• C. If both, statement I and statement II are needed to answer the question
• D. If the question cannot be answered even with the help of both the statements

Hint:

Use both resource constraints and demand requirements to set up inequalities, then solve for equality.

Answer 1

The Correct Option is C

Let the number of widgets of type A be \( a \) and type B be \( b \).
From Statement I: Each unit of A uses 2 machine hours, each unit of B uses 4.
Total machine hours: \( 2a + 4b \leq 80 \) — but no information about values of \( a \) and \( b \).
From Statement II: Dealer demands at least 10 units of A: \( a \geq 10 \)
Dealer demands at least 15 units of B: \( b \geq 15 \)
Still, we cannot determine the exact value of \( a \).
Using both I and II: We combine constraints: \( a \geq 10 \), \( b \geq 15 \) and \( 2a + 4b \leq 80 \)
Substitute \( b = 15 \) (minimum allowed), we get: \( 2a + 4(15) \leq 80 2a + 60 \leq 80 2a \leq 20 a \leq 10 \)
But also, \( a \geq 10 \). So the only feasible value is: \[ \boxed{a = 10} \]