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4 years ago

11

What is 36.25 + 40.30

1 answer:

melamori03 [73]4 years ago

3 0

36.25 + 40.30 = 76.55

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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

Cerrena [4.2K]

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

$R(x,y) = 100x-34x^2+8xy+50y-16y^2$

In order to maximize the revenue, set

$R_x=0, \ \ \ R_y=0$

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

$R_x=0$

$68x-8y=100$ .............(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

4 0

3 years ago