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Manufacture has been selling 1450 television sets a week at $540 each. A market survey indicates that for each $13 rebate offered to a buyer, the number of sets sold will increase by 130 per week.
a) Find the function representing price as a function of the demand p(x)p(x), where xx is the number of the television sets sold per week and p(x)p(x) is the corresponding price.

Respuesta :

Answer:

[tex]p(x)= -\frac{1}{10}x + 685[/tex]

Step-by-step explanation:

Since, Function of demand is the linear function of quantity.

Let x represents the quantity and p represents the price of each unit.

∵ Manufacture has been selling 1450 television sets a week at $540 each,

i.e. [tex](x_1, p_1) = (1450, 540)[/tex]

Also, for each $13 rebate offered to a buyer, the number of sets sold will increase by 130 per week.

i.e. [tex](x_2, p_2) = (1580, 527)[/tex]

Thus, the linear equation of the price,

[tex]p-p_1 = \frac{p_2-p_1}{x_2-x_1}(x-x_1)[/tex]

[tex]p-540 = \frac{527 - 540}{1580-1450}(x-1450)[/tex]

[tex]p-540 = -\frac{13}{130}(x-1450)[/tex]

[tex]p-540 = -\frac{1}{10}(x-1450)[/tex]

[tex]p = -\frac{1}{10}x + 145 + 540[/tex]

[tex]\implies p = -\frac{1}{10}x + 685[/tex]

Hence, the function representing price as a function of the demand is,

[tex]p(x)= -\frac{1}{10}x + 685[/tex]

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