I need help with this qurstion -2 (4z - 4) = 10 - 6z
2 answers:
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Answer:
(a) A(x) = 100x + 1100
(b) x = 2.5 USD
(c) A(x) = 100x + 1100 and x = -1.5 USD
Step-by-step explanation:
(a) Since there's a linear relation between weekly sales A(x) and the discount, we can model it as the following expression
A(x) = mx + b
where x is the discount, m is the slope and b is the intersect of the linear equation. We can solve for slope first
To solve for b, we can just plug in m = 100, x = 0 and A(0) = 1100
1100 = 100*0 + b
b = 1100
Therefore A(x) = 100x + 1100
With discount x, the actual price would then be p - x. Where p is the original undiscounted pricing ($16 in this case)
And with sale A(x), the revenue would then be
To find the maximum value of this, we can take the 1st derivative and set it to 0
R' = -200x + 100p - 1100 = 0
200x = 100p - 1100
when p = $16 then x = 0.5*16 - 5.5 = 8 - 5.5 = 2.5 USD
(c) when the price p is $8 then A(x) would sill be 100x + 1100 because it doesn't depend on p, but the discount. But to maximize the revenue, x will need to be
0.5p - 5.5 = 0.5*8 - 5.5 = 4 - 5.5 = -1.5 USD
So the Pizza owner would need to raise the price by 1.5 USD because originally the pizza is already inexpensive.
Answer:
The answer is
Step-by-step explanation:
Given: f(x) = 3 + 2x - x²
To compute f(3 + h) substitute x = 3 + h.
Similarly, to compute f(h) simply substitute x = h.
We are asked to compute
f(3 + h) = 3 + 2(3 + h) - {(3 + h)²}
= 3 + 6 + 2h - {9 + 6h + h²}
= 9 + 2h - 9 - 6h - h²
= - 4h - h²
Now, f(h) = 3 + 2h - h²
f(3 + h) - f(h) = -4h - h² - 3 - 2h + h²
= -6h - 3
which is the required answer.