Answer:
Step-by-step explanation:
Let call:
x₁ number of units of product 1
x₂ number of units of product 2
We build the next table
metal frame electrical components Profit $/u
Product 1 (x₁) 1 2 13
Product 2 (x₂) 3 2 26(*)
Total supply ( in units) 3000 4500
(*) Up to 900 units . each unit above that number has to be ruled out
From the above table we have:
Objective function z
z = 13*x₁ + 26*x₂ to maximize
1*x₁ + 3*x₂ ≤ 3000
2*x₁ + 2*x₂ ≤ 4500
x₁ ≥ 0 ; 900 ≥ x₂ ≥ 0
Rearranging
z - 13* x₁ - 26*x₂ = 0
0 + x₁ +3*x₂ ≤ 0
0 + 2*x₁ +2*x₂ ≤ 0
x₁ ≥ 0
0 ≤ x₂ ≤ 900
Or
z - 13* x₁ - 26*x₂ = 0
0 + x₁ +3*x₂ + s₁ + 0s₂ = 0
0 + 2*x₁ +2*x₂ + 0s₁ + s₂ = 0
x₂ + 0s₁ + 0s₂ + s₃ = 900
x₁ ≥ 0 x₂ ≥ 0
And the table is ready for use Simplex Method
Answer:
20 miles per hour
Step-by-step explanation:
traveling against the wind was 160mph (400/2.5)
traveling with the wind was 200mph (400/2)
going against the wind is going in the negative direction of the wind speed, and going with the wind is going in a positive direction of the wind speed, therefore the wind speed is |direction1-direction2|/2, which would be |200-160|/2 = |40|/2 = 20mph
(180mph is neutral speed with no wind, with wind affecting this neutral speed ±20mph)
First multiply each term by 24(the common denominator found by 8×3) to remove the fractions and make things easier.
This will give you,
Then just continue to simplify and isolate the variable.
Given:
...(i)
For 
.
To find:
The nth term for the given recursive formula.
Solution:
The given recursive formula is of the form of
...(ii)
It is the recursive formula of a GP, where r is common ratio.
On comparing (i) and (ii), we get
Now,
First term: 
Common difference:
nth term of a GP is
Putting a=3 and r=2, we get
Therefore, the equation for the nth term is .
-12n + 17 = 23
-17 -17
-12n = 6
/-12 /-12
N = - 1/2
N = -.5
