Answer:
Price = $4.50
Maximum revenue = $2,430
Step-by-step explanation:
The concession stand sells 600 bags of peanut at $4.00 (600, $4.00).
If there is a $1 increase in price, the number of bags old will decrease by 120, which mens that 480 bags of peanuts will be sold at $5.00 (480, $5.00).
Tracing a linear relationship between price and quantity sold with the two given points:
![m = \frac{5-4}{480-600}\\ m=-\frac{1}{120}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B5-4%7D%7B480-600%7D%5C%5C%20m%3D-%5Cfrac%7B1%7D%7B120%7D)
![P - P_0=m*(Q-Q_0)\\P-4.00=-\frac{1}{120} (Q-600)\\P= -\frac{1}{120}Q +9](https://tex.z-dn.net/?f=P%20-%20P_0%3Dm%2A%28Q-Q_0%29%5C%5CP-4.00%3D-%5Cfrac%7B1%7D%7B120%7D%20%28Q-600%29%5C%5CP%3D%20-%5Cfrac%7B1%7D%7B120%7DQ%20%2B9)
The revenue function is given by the price multiplied by the quantity sold:
![R=Q*P= (-\frac{1}{120}Q +9)*Q\\R=-\frac{1}{120}Q^2 +9Q](https://tex.z-dn.net/?f=R%3DQ%2AP%3D%20%28-%5Cfrac%7B1%7D%7B120%7DQ%20%2B9%29%2AQ%5C%5CR%3D-%5Cfrac%7B1%7D%7B120%7DQ%5E2%20%2B9Q)
The value of 'Q' for which the derivate of the revenue function is zero, is the output level for which revenue is maximum:
![R'=0=-\frac{2}{120}Q+9\\Q_{max} = 540\\P_{max} = -\frac{540}{120} +9\\P_{max} =\$4.50](https://tex.z-dn.net/?f=R%27%3D0%3D-%5Cfrac%7B2%7D%7B120%7DQ%2B9%5C%5CQ_%7Bmax%7D%20%3D%20540%5C%5CP_%7Bmax%7D%20%3D%20-%5Cfrac%7B540%7D%7B120%7D%20%2B9%5C%5CP_%7Bmax%7D%20%3D%5C%244.50)
The total revenue of 540 units at $4.50 per unit is:
![R = \$4.50*540\\R=\$2,430](https://tex.z-dn.net/?f=R%20%3D%20%5C%244.50%2A540%5C%5CR%3D%5C%242%2C430)
Answer is .5
Step-by-step explanation:
I believe the equation for this graph is: Y= |x- (-2)| + 3
Answer:
<em>Explanation below</em>
Step-by-step explanation:
<u>Angles in a Triangle</u>
There are two basic relations of angles we need to recall:
- Supplementary angles add up to 180°
- Internal angles of a triangle add up to 180°
Note a, b, and c are the internal angles of the triangle. The angle c is what is needed to a+b to complete 180°, thus:
c = 180 - ( a + b )
Also, note c and d are supplementary angles. Again, c is what is needed to d to complete 180°, thus
c = 180 - d
From the two relations above, it follows that:
a + b = d
Answer: 3/4
Step-by-step explanation: 3/4 equals .75