Question:
A company sells two types of notebooks, A and B. Each notebook requires two processes: printing and binding. Notebook A requires \(2\) minutes for printing and \(1\) minute for binding. Notebook B requires \(4\) minutes for printing and \(2\) minutes for binding. The company can spend \(6\) hours on printing and \(2\) hours on binding. If the profit made on notebooks A and B is Rs. \(2\) and Rs. \(5\) respectively, then the Linear Programming Problem (LPP) to maximize the total profit \(z\) is ...
A company sells two types of notebooks, A and B. Each notebook requires two processes: printing and binding. Notebook A requires \(2\) minutes for printing and \(1\) minute for binding. Notebook B requires \(4\) minutes for printing and \(2\) minutes for binding. The company can spend \(6\) hours on printing and \(2\) hours on binding. If the profit made on notebooks A and B is Rs. \(2\) and Rs. \(5\) respectively, then the Linear Programming Problem (LPP) to maximize the total profit \(z\) is ...
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Convert hours to minutes and write printing and binding constraints for x notebooks A and y notebooks B.
Updated On: Nov 12, 2026
- maximize \(z=2x+5y\) subject to \(2x+y\leq 360,4x+2y\leq 120,x\geq 0,y\geq 0\)
- maximize \(z=2x+5y\) subject to \(2x+y\leq 120,4x+2y\leq 360,x\geq 0,y\geq 0\)
- maximize \(z=2x+5y\) subject to \(2x+4y\leq 360,x+2y\leq 120,x\geq 0,y\geq 0\)
- maximize \(z=2x+5y\) subject to \(2x+4y\leq 120,x+2y\leq 360,x\geq 0,y\geq 0\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
Let \(x\) be the number of notebooks A and \(y\) the number of notebooks B. Profit is \(z=2x+5y\).
Step 2: Convert time
Printing: 6 hours is 360 minutes. Binding: 2 hours is 120 minutes.
Step 3: Constraints
Printing: \(2x+4y\leq 360\).
Binding: \(x+2y\leq 120\).
Also \(x\geq 0,\ y\geq 0\).
Step 4: Compare the options
This matches the third option.
Final Answer:
The LPP maximises \(z=2x+5y\) subject to \(2x+4y\leq 360,\ x+2y\leq 120,\ x,y\geq 0\). \[ \boxed{\text{(C) }\text{maximize }z=2x+5y\text{ subject to }2x+4y\leq 360,x+2y\leq 120,x\geq 0,y\geq 0} \]
Let \(x\) be the number of notebooks A and \(y\) the number of notebooks B. Profit is \(z=2x+5y\).
Step 2: Convert time
Printing: 6 hours is 360 minutes. Binding: 2 hours is 120 minutes.
Step 3: Constraints
Printing: \(2x+4y\leq 360\).
Binding: \(x+2y\leq 120\).
Also \(x\geq 0,\ y\geq 0\).
Step 4: Compare the options
This matches the third option.
Final Answer:
The LPP maximises \(z=2x+5y\) subject to \(2x+4y\leq 360,\ x+2y\leq 120,\ x,y\geq 0\). \[ \boxed{\text{(C) }\text{maximize }z=2x+5y\text{ subject to }2x+4y\leq 360,x+2y\leq 120,x\geq 0,y\geq 0} \]
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