RekiHyanidn
Answered

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A garments store sells about 40 t-shirts per week at a price of Php 100 each.
For each P10 decrease in price, the sales lady found out that 5 more t-shirts per were sold.

a. Write a quadratic function in standard form that models the revenue from t-shirts sales.
b. What price produces the maximum revenue?​

Sagot :

ShadowSonicidn

[tex]{\color{magenta}{———————————————————————————}}[/tex]

A garments store sells about 40 t-shirts per week at a price of Php 100 each. For each P10 decrease in price, the sales lady found out that 5 more t-shirts per were sold.

[tex]{\color{magenta}{———————————————————————————}}[/tex]

A. Write a quadratic function in standard form that models the revenue from t-shirts sales.

SOLUTION:

[tex]\\ \large\sf\bold{}{ \:\:\: \:\:\:Revenue\:R(x)=(40+5x)(100-10x)}[/tex]

[tex]\\ \sf\large\bold{}{\:\:\:\:\:\:R(x)=-50x²+100+4000}[/tex]

[tex]\\ \large\sf\bold{}{\:\:\:\:\:\:R(x)=-50(x-1)²+{\color{green}{4050}}}[/tex]

Thus, the maximum revenue is Php 4050.

[tex]{\color{magenta}{———————————————————————————}}[/tex]

B. What price produces the maximum revenue?

SOLUTION:

The price of the t-shirt to produce maximum revenue can be determined by

[tex]\\ \sf\large\bold{}{\:\:\:\:\:\:P(x) = 100 – 10x}[/tex]

[tex]\\\sf\large\bold{}{\:\:\:\:\:\:P(x) = 100 – 10 (1) ={\color{green}{90}}}[/tex]

Thus, Php 90 is the price of the t-shirt that produces maximum revenue.

[tex]{\color{magenta}{———————————————————————————}}[/tex]

Hope it may help you⚘

꧁___ShadowSonic___꧂

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