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mem8163
14.12.2019 •
Mathematics
The restaurant can charge $1.09 for a 3 ounce burger and $1.59 for a 5 ounce burger. if it projects to sell 3000 burgers in a week, which size burger should it sell?
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Ответ:
Ответ:
y = -x + 5 and y = -x - 7 (see attached graph)
Step-by-step explanation:
y =![\frac{9}{x + 1}](/tpl/images/0052/2128/3979d.png)
= 9(x + 1)⁻¹
Use the product rule to find the derivative
a = 9 a' = 0
b = (x + 1)⁻¹ b' = -(x + 1)⁻²
ab' + a'b
= 9[-(x + 1)⁻²] + 0[(x + 1)⁻¹ ]
=![\frac{-9}{(x + 1)^{2}}](/tpl/images/0052/2128/f1662.png)
Set the derivative equal to the desired slope of -1 to solve for x
-1 =![\frac{-9}{(x + 1)^{2}}](/tpl/images/0052/2128/f1662.png)
-(x + 1)² = -9
(x + 1)² = 9
√(x + 1)² = √9
x + 1 = +/- 3
x + 1 = 3 x + 1 = -3
x = 2 x = -4
Plug those values into the original equation to solve for y:
y =![\frac{9}{x + 1}](/tpl/images/0052/2128/3979d.png)
=![\frac{9}{2 + 1}](/tpl/images/0052/2128/8dbf2.png)
= 3
(2, 3)
y =![\frac{9}{x + 1}](/tpl/images/0052/2128/3979d.png)
=![\frac{9}{-4 + 1}](/tpl/images/0052/2128/f1558.png)
= -3
(-4, -3)
Next, plug in the given slope (-1) and the coordinates above into the Point-Slope formula y - y₁ = m(x - x₁) to find the equations:
m = -1, (x₁ y₁) = (2, 3) m = -1, (x₁ y₁) = (-4, -3)
y - 3 = -1(x - 2) y + 3 = -1(x + 4)
y - 3 = -x + 2 y + 3 = -x - 4
y = -x + 5 y = -x - 7