Answer:
z (min) = 360 x₁ = x₃ = 0 x₂ = 3
Step-by-step explanation:
Protein Carbohydrates Iron calories
Food 1 (x₁) 10 1 4 80
Food 2 (x₂) 15 2 8 120
Food 3 (x₃) 20 1 11 100
Requirements 40 6 12
From the table we get
Objective Function z :
z = 80*x₁ + 120*x₂ + 100*x₃ to minimize
Subjet to:
Constraint 1. at least 40 U of protein
10*x₁ + 15*x₂ + 20*x₃ ≥ 40
Constraint 2. at least 6 U of carbohydrates
1*x₁ + 2*x₂ + 1*x₃ ≥ 6
Constraint 3. at least 12 U of Iron
4*x₁ + 8*x₂ + 11*x₃ ≥ 12
General constraints:
x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers
With the help of an on-line solver after 6 iterations the optimal solution is:
z (min) = 360 x₁ = x₃ = 0 x₂ = 3
10 less than 5 times the value of a number -> 5a - 10
10 times the quantity of 12 more than one-fourth of a number -> 10(12+1/4a)
We have :
5a - 10 = 10(12 + 1/4a)
5a - 10 - [10(12 + 1/4a)] = 0
5a - 10 - (120 + 5/2a) = 0
5a -10 - 120 - 5/2a = 0
Group : (5a-5/2a) - (10 + 120) = 0
5/2a - 130 = 0
5/2a = 130 -> a = 130 : 5/2 = 52
Recheck : 5 x 52 - 10 = 250
10 x (12 + 1/4 x 52) = 10 x (12 + 13) = 10 x 25 = 250
This is the concept of geometry, the congruence statements that can be evaluated from the parallel figure is:
DH=HF
EH=HG
EF=DG
DE=FG
hence;
Hence ΔDEF is congruent to ΔDGF and ΔEFG is congruent to ΔEGD by Side-side-side (SSS) postulate
If you need to solve this equation you can multiply the both side of equation on (-1). Like that
<span>2 = (-x);
-1·2 = (-1)·(-x)
if you multiply negative and </span><span>positive </span>you'll have negative,
if you multiply negative and <span>negative you'll have </span><span><span>positive. So
</span>
</span>-2 = x. or
x = -2.
The answer is -2.
<span>Division is the inverse operation of multiplication.</span>