The greatest common divisor of positive integers $m$ and $n$ is 8. the least common multiple of $m$ and $n$ is 112. what is the least possible value of $m n$?

8 and 112.

Step-by-step explanation:

as gcd(m,n) = 8 we have that m and n are multiples of 8. Now, as both are multiples of 8 the least common multiple will be the greatest between m and n.

Then, as we need 112 to be the least common multiple m or n has to be 112. Now, the smallest number that is a multiple of 8 is 8. Then, m and n need to be 112 and 8.

gcd(112,8) = 8

lcm(112,8) = 112.

Then, 8 and 112 are the least possible values of m and n.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

step-by-step explanation: