Question

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.

Answer 1

`p(x)= -(1)/(10)x + 685`

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.
`(x_1, p_1) = (1450, 540)`

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

i.e.
`(x_2, p_2) = (1580, 527)`

Thus, the linear equation of the price,

`p-p_1 = (p_2-p_1)/(x_2-x_1)(x-x_1)`

`p-540 = (527 - 540)/(1580-1450)(x-1450)`

`p-540 = -(13)/(130)(x-1450)`

`p-540 = -(1)/(10)(x-1450)`

`p = -(1)/(10)x + 145 + 540`

`\implies p = -(1)/(10)x + 685`

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

`p(x)= -(1)/(10)x + 685`