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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.
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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.
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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.
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Hope it may help you⚘
꧁___ShadowSonic___꧂
