Question

A concert-promoting company has been selling an average of 175 T-shirts at performances for $23 each. The company estimates that for each dollar that the price is lowered, an additional 25 shirts will be sold. Let x be the number of shirts sold. Find the demand function for the shirts.

Answer 1

The demand function for the shirts of a concert-promoting company which has been selling an average of 175 T-shirts at performances for $23 each is y=175-6.08x.

What is demand function?

The demand function is the function

$Q=a-bP$

Here, Q is linear demand curve, a factor which influence the demand, b is slope and P is price.

A concert-promoting company has been selling an average of 175 T-shirts at performances for $23 each. Thus, the total selling price is,

$P=175\times23\\P=4025$

The company estimates that for each dollar that the price is lowered, an additional 25 shirts will be sold.  Thus, the total number of

$23=175-25b\\23-175=-25b\\b=\dfrac{152}{25}\\b=6.08$

Put the values in, the function for X number of shirt and y price,

$y=175-6.08x$

Hence, the demand function for the shirts of a concert-promoting company which has been selling an average of 175 T-shirts at performances for $23 each is y=175-6.08x.

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