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BARSIC [14]
3 years ago
10

Someone solve this for me please

Mathematics
1 answer:
Butoxors [25]3 years ago
5 0

Answer:

x=2; y=1

Step-by-step explanation:

Since the triangle is equilateral, which means three sides have the same length.

So we have:4x-y=2x+3y=7

4x-y=2x+3y\\4x-y+y=2x+3y+y\\4x=2x+4y\\2x=4y\\x=2y\\

Since 2x+3y=7 and plug in x=2y

we have

2x+3y=7\\2(2y)+3y=7\\4y+3y=7\\7y=7\\y=1

and since y=1

x=2

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A concession stand at an athletic event is trying to determine how much to sell cola and iced tea for in order to maximize reven
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Solution :

Demand for cola : 100 – 34x + 5y

Demand for cola : 50 + 3x – 16y

Therefore, total revenue :

x(100 – 34x + 5y) + y(50 + 3x – 16y)

R(x,y)  = $100x-34x^2+5xy+50y+3xy-16y^2$

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In order to maximize the revenue, set

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$R_x=\frac{dR }{dx} = 100-68x+8y$

$R_x=0$

$68x-8y=100$  .............(i)

$R_y=\frac{dR }{dx} = 50-32x+8y$

$R_y=0$

$8x-32y=-50$  .............(ii)

Solving (i) and (ii),

4 x (i)    ⇒       272x - 32y = 400

     (ii)   ⇒   (-<u>)     8x - 32y = -50   </u>

                        264x        = 450

∴   $x=\frac{450}{264}=\frac{75}{44}$

     $y=\frac{175}{88}$

So, x ≈  $ 1.70      and    y = $ 1.99

    R(1.70, 1.99) = $ 134.94

Thus, 1.70 dollars per cola

          1.99 dollars per iced ted to maximize the revenue.

Maximum revenue = $ 134.94

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