Find the minimum value of the function for the polygonal convex set determined by the given system of inequalities.
1 answer:
Answer:
Option b (4,1)
Step-by-step explanation:
The region given by the system of inequalities is shown in the graph. We must look within this region for the point that minimizes the objective function
The minimum points are found in the lower vertices of the region.
These vertices are found by equating the equations of the lines::
-------------------
---------------------
The lower vertices are:
(4, 1) (2, 4)
Now we substitute both points in the objective function to see which of them we get the lowest value of
Then the value that minimizes f(x, y) is (4,1).
Option b
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Answer:
c(p) = {0.2 p ⇒ p < 1000
0.24 p - 40 ⇒ 1000 ≤ p ≤ 2000
0.29 p - 140 ⇒ p > 2000}
Step-by-step explanation:
* Lets explain how to solve the problem
- The profit is represented by p
1. If the profit is under $1,000, the commission rate is 20%
∵ The profit is p < 1000
∵ 20% of p = = 0.2 p
∵ c(p) is the function of the commission
∴ c(p) = 0.2 p when p < 1000
2. If the profit is at least $1,000 and less than or equal to $2,000, the
commission rate is 20% of the first $1,000 and 24% of the remainder
of the profit
- At least means greater than or equal
∵ The profit 1000 ≤ p ≤ 2000
- The commission is divided into 20% of first $1000 and 24% of
the reminder
∵ 20% of 1000 = = 200
∵ The remainder of the profit = p - 1000
∵ 24% of the remainder profit =
= 0.24(p - 1000) = 0.24 p - 240
∴ The total commission = 200 + 0.24 p - 240
∴ The total commission = 0.24 p - 40
∴ c(p) = 0.24 p - 40 when 1000 ≤ p ≤ 2000
3. If the profit is above $2,000, the rate is 20% of the first $1,000
of profit, 24% of the next $1,000 of profit, and 29% of the amount
of profit over $2,000
∵ The profit p > 2000
- The commission is divided into 20% of first $1000 and 24% of the
next $1,000 of profit, and 29% of the amount of profit over $2,000
∵ 20% of 1000 = = 200
∵ 24% of 1000 = = 240
- The amount of profit over $2,000 = p - 2000
∵ 29% of the amount of profit over $2,000 =
= 0.29(p - 2000)
= 0.29 p - 580
∴ The total commission = 200 + 240 + 0.29 p - 580
∴ The total commission = 0.29 p - 140
∴ c(p) = 0.29 p - 140 when p > 2000
* The commission function is:
c(p) = {0.2 p ⇒ p < 1000
0.24 p - 40 ⇒ 1000 ≤ p ≤ 2000
0.29 p - 140 ⇒ p > 2000}
Check the picture below.
so to find the surface area of the triangular prism, we simply add the areas of each of the figures composing it, as you can see is really just 2 triangles an 3 rectangles.
now, to get the volume is simply the area of the triangular face times the length, well, we know the area of one of the triangles is 6, times 10 is just 6*10 = 60.
