Question

Two machines of the same production rate are available for use. On machine 1, the fixed cost is Rs. 100 and the variable cost is Rs. 2 per piece produced. The corresponding numbers for machine 2 are Rs. 200 and Re. 1 respectively. For certain strategic reasons both the machines are to be used concurrently. The sale price of the first 800 units is Rs. 3.50 per unit and subsequently it is only Rs. 3.00. The breakeven production rate for each machine is

• A. 75
• B. 600
• C. 150
• D. 100

Answer 1

The correct option is A 75


Let x be the quantity produced by each machine.

$\therefore \text{The total cost in production using machine - 1,}$

$T{C}_1=\text{Fixed cost + Variable cost}$

$=100+2\left(x\right)=100+2x$

$\therefore \text{Total cost in production using machine - 2,}$

$T{C}_2=\text{Fixed cost + Variable cost}$

$=200+1\left(x\right)=200+x$

$\because \text{At break-even point,}$

$\text{Total sales price = Total cost in production}$

$3.5\times 2x=T{C}_1+T{C}_2$

$7x=100+2x+200+x$

$7x=300+3x$

$x=75$

Now, quantity,

$\text{x = 75 units (< 800 units)}$

If the value of x comes out > 800 units then the next unit sale price will be Rs. 3.