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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.

The revenue Y received for selling t DVD players is given by the equation Y 11000 t2 10t Find the number of DVD players that must be sold to obtain the maximum class=

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MrRoyal

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

How to determine the number of DVDs?

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

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