Revenue suppose that the manufacturer of a gas clothes dryer...

Revenue Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is $p$ dollars, the revenue $R($ in dollars) is $$ R(p)=-4 p^{2}+4000 p $$ (a) At what prices $p$ is revenue zero? (b) For what range of prices will revenue exceed $\$ 800,000 ?$

Transcript

00:01 This question, suppose revenue, suppose that the manufacturer of a gas floats dryer has found that when a unit price is p dollars, then the revenue is given by this particular equation.

00:12 So we need to find the value of price p when the revenue is zero.

00:16 So we need to equate r to zero.

00:18 This means that we need to equate negative 4p square plus 4 ,000 p to zero, which means that p is taken out and we are left with negative 4p plus 4 ,000 to 0, which means that p is taken out and we are left with negative 4p plus 4 ,000.

00:30 Is equal to 0 which means that either the value of price is 0 or negative 4p plus or negative 4p plus 4 ,000 is equal to 0 this means that the value of p is $1 ,000 so p equal to 0 doesn't really make any sense because the unit price cannot really be zero dollars that's practically it doesn't make any sense so the answer is $1 ,000 and then for what range of price for the revenue exceed $800 ,000 dollars so here remember that r is already in in in in r is in dollars so remember about that so we need to find the value such that negative 4p square plus 4 ,000 p is actually greater than 800 ,000 so we're going to divide both sides by four and bring this over to the left so this becomes minus p square plus 1000 p minus two followed by five zero this should be better than zero so multiplying minus one both sides so we have p square minus 1 ,000 p plus 200 ,000 should be less than zero all right let's see if we can factorize this i think we can because 200 000 can be written as 200 times 1000 but that's not really gonna help us let's see i think it's a better idea to just use quadratic formula to find the roots so the quadratic rules formula the roots are gonna be a 1000 plus minus square root of 1 ,000 square minus 4 times 200 ,000 over 2 times 1 so let me just just grab my calculator over here so that's four times 200 ,000 and 1 ,000 square minus answer and the square root of this is going to be this value so either we have 1 ,000 minus this over 2 which is coming as 276 .39 and the other value of p is coming as this is multiplied with 2 and subtracted by 1000.

03:12 The value is coming as 1000 minus answer over 2, which is coming as 723 .7 .63...

Question

Revenue Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is $p$ dollars, the revenue $R($ in dollars) is $$ R(p)=-4 p^{2}+4000 p $$ (a) At what prices $p$ is revenue zero? (b) For what range of prices will revenue exceed $\$ 800,000 ?$

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