The demand function p = D ( x ) and the total cost function...

The demand function p = D ( x ) and the total cost function C ( x ) for a particular commodity are given in terms of the level of production x as D ( x ) = -0.03x + 41 C ( x ) = 1.87x^2 + 18.3x + 15.4 Part 1 a. Find the revenue function R ( x ). The revenue function is R ( x ) = -0.03x^2 + 41x . Part 2 a. Find the profit function P ( x ). The profit function is P ( x ) = -1.90x^2 + 22.7x - 15.4 . Part 3 out of 3 b. Find all values of x for which production of the commodity is profitable. The production of the commodity is profitable when . Express your answer as an inequality. Round any decimal answers to two decimal places.

Transcript

00:01 Okay, in this sum they gave the demand function d of x, which is nothing but minus 0 .03 times x plus 41.

00:16 Okay, and they also gave a cost function, c of x, which is nothing but 1 .87 x squared plus 18 .3x plus 15 .3x plus 15.

00:32 Point four okay now they wanted us to find out revenue function someone already did it it is correct by the way what is there any function this is nothing but demand okay demand is nothing but the price times times the quantity okay this is the revenue so how much will we get minus zero 0 .03 x squared plus 41 x this is what they gave okay what you already answered and for the second part it is profit p of x which is nothing but the revenue function minus the cost function that's how we calculate profit so what is it 0 .03 x square plus 41 times x minus 1 .87 x square plus 18 .3x plus 15 .4 which gives us minus 1 .9 x square plus 22 point sorry this this has to be minus yeah 22 .7 7x minus minus 15 .4 okay this is is the profit function now we are diving into the actual part of the question where we have to find out the values of x for which production of commodities profitable okay we have to express our answer in inequality so well let's just do that we have to find out when profit is greater than zero okay okay we have to find this value greater than equal it would be profitable if it would be profitable if it only if the profit value is greater than 0 correct so now let's just do the inequality minus 1 .9 x square plus 22 .7 times x minus 15 .4 is greater than equal to 0 now i'm multiplying it by minus 1 so the inequality changes minus 22 .7x plus 15 .4 less than 0 .0.

03:24 Okay the inequality changes now now we have to factorize it to factorize it we have to simply use this quadratic equation formula four times a times c divided by two a okay if i do this if i do this i would get 22 .7 lesser minus root over 51529 okay, i would write it actually, i'll simplify it later.

04:08 Square minus four times 1 .9 times 15 .4.

04:19 Okay, divided by 2 times 1 .9.

04:26 So basically, you'll get two values for this...

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