 Hello and how are you all today? The question says the calculator manufacturing companies find that the daily cost of producing X-calculator is given by C is equal to 200X plus 7500. Firstly, if each calculator is sold for Rs. 350, find the minimum number of calculator that must be produced daily and sold to ensure no loss. Secondly, if the selling price increased by Rs. 150, what would be the break-even point? So, let us proceed with our solution. Now here, let X-calculators are produced in a day. So, we are given the cost of producing these X-calculators that is the cost of, that is the cost function 200X plus 7500. We are given that each calculator is sold for Rs. 350. So, that means price of the calculator that is P is given to us as 350. So, we can easily find out the revenue function as, as we are producing X-calculators and selling X also daily. So, that means it will be priced into quantity that we have sold that is X. So, it will be 350 into X that is 350X. Further, we need to find out the minimum number of calculators that must be produced daily and sold to ensure no loss. So, for no loss, revenue function should always be greater than the cost function or equal to it to ensure that we are not having any loss. So, it can be greater than equal to the cost function. So, this implies 350X is greater than equal to 200X plus 7500. This further implies that 150X is greater than equal to 7500 that is X is always greater than equal to 7500 divided by 150 that is 50. So, a company should make more than 50 calculators or equal to 50 calculators to ensure no loss. That is it may be 51 calculators, 52 calculators and so on. So, this completes the first part of the question that is given to us. Further, we are given that for the second part, selling price is increased by rupees 150. This means that now the price of calculator will be previously it was 350. Now, add 150 to it. So, now it will be rupees 500. So, this means our revenue function is changed from 350X to 500. So, for break-even points, this function should be equal to our revenue function. This is a case where the firm is not incurring any loss, earning any profit also. That means it is a no loss, no profit situation. Remember, this is the meaning of break-even point. So, let us equate it. Our cost function has not changed. So, it is 200X plus 7500 and our new revenue function is 500X. So, it is further equal to 7500 is equal to 300X. That further implies that the value of X is now 25. So, we can write that if the selling price is increased by rupees 150, the break-even point is when the firm is producing and selling 25 calculators. Right. So, this completes the second part also. Hope you understood it well and enjoyed it too. Have a nice day.