 Hello and welcome to the session. Let's discuss the following question. It says the total cost and the total revenue of a firm that produces and sells x units of its product daily are expressed as cx is 5x plus 350 and rx is 50x minus x square. Calculate the break even points and the number of units the firm will produce which will result in loss. So let's now move on to the solution. We are given that the cost function is 5x plus 350 and the revenue function is 50x minus x square. Now we have to find the break even points. Now at break even points cost function is equal to the revenue function. So we have 5x plus 350 is equal to 50x minus x square. So we have this implies 50x minus x square minus 5x minus 350 is equal to 0 and this implies minus x square plus 45x minus 350 is equal to 0. Now taking minus sign common we have x square minus 45x plus 350 is equal to 0. Now we'll factorize this quadratic equation. So we have x square minus 35x minus 10x plus 350 is equal to 0. Now taking x common from the first two terms we have x into x minus 35 taking minus 10 common from the last two terms we have x minus 10 into x minus 35 is equal to 0. Now taking x minus 35 common we have x minus 35 into x minus 10 is equal to 0. So this implies x minus 35 is equal to 0 or x minus 10 is equal to 0 and this implies x is equal to 35 or x is equal to 10. So these are the break even points and this is the answer to the first part of the question. Now in the second part we have to calculate the number of units the firm will produce which will result in loss. Now for loss the revenue function should be less than the cost function for loss rx must be less than cx. Now rx is 50x minus x square and this is less than the cost function which is 5x plus 350. So this implies 5x plus 350 plus x square minus 50x is greater than 0. This implies x square minus 45x plus 350 is greater than 0. Now this is the same quadratic equation we got in the first part and it gets factorized as x minus 10 into x minus 35 greater than 0. So this implies x minus 10 is greater than 0 and x minus 35 is greater than 0 or both are less than 0 that is both factors are less than 0 then their product will be greater than 0. So now we take two cases x minus 10 greater than 0 and x minus 35 greater than 0. So this implies x is greater than 10 and this implies x is greater than 35. So the company will be in loss if it produces the units greater than 35 since it says that x is greater than 10 x is greater than 35. So the common x greater than 35 now case 2 x minus 10 less than 0 x minus 35 less than 0. So x is less than 10 x is less than 35. So again the company will be in loss if it produces the units less than 10 less than 35. So the common x less than 10 x 4 or hence will be in loss 35. So this completes the question and the session. Bye for now. Take care. Have a good day.