It is known that a laptop company's average production is given by P(t) = (150t) / (3t+20), where t is the time (in days). How many days will it take the company to produce 30 laptops?

Step-by-step explanation:

Step one:

given that the expression for the company's average production is

Required:

t, when P=30

Step two:

substituting we have

30=150t/3t+20

cross multiply we have

30(3t+20)=150t

90t+600=150t

collect like terms

600=150t-90t

600=60t

divide through by 60

t=600/60

t=10 days

it will take the company 10 days

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