The revenue, Y, received for selling, t, DVD players is given by the equation: Y = -1/1000 t^2 + 10t. Find the number of DVD players that must be sold to obtain the maximum revenue.

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MrRoyal MrRoyal · Answer 1 · 2022-04-01T13:22:09+02:00

The equation Y = -1/1000 t^2 + 10t is an illustration of a quadratic function

The number of DVD players that must be sold to obtain the maximum revenue is 5000

The equation of the function is given as:

[tex]Y = -\frac 1{1000} t^2 + 10t[/tex]

Differentiate the function

[tex]Y' = -2 * \frac 1{1000} t + 10[/tex]

Set to 0

[tex]-2 * \frac 1{1000} t + 10 = 0[/tex]

Simplify

[tex]- \frac 1{500} t + 10 = 0[/tex]

Subtract 10 from both sides

[tex]- \frac 1{500} t = -10[/tex]

Multiply both sides by -500

[tex]t = 5000[/tex]

Hence, the number of DVD players that must be sold to obtain the maximum revenue is 5000