Which are correct representations of the inequality -3(2x - 5) <5(2 - x)? Select two options.
2 answers:
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Answer: We can arrange the steps with help of below explanation.
Step-by-step explanation:
Here ABC is a triangle,
Draw a perpendicular from BD to side AC ( construction)
where
In the right triangle BCD, from the definition of cosine:
cos C =CD/ BC
CD= a cos C
Subtracting this from the side b, we see that
DA= b-acos C
In the triangle BCD, from the definition of sine:
sin C =BD / a
BD = a sin C
In the triangle ADB, applying the Pythagorean Theorem
Substituting for BD and DA from (2) and (3)
⇒ ( On simplification)
⇒
⇒
⇒ (because,
)
Given:
Product A requires 7 board feet of wood and 4 lbs of wicker.
Product B requires 5 board feet of wood and 5 lbs of wicker.
Product C requires 4 board feet of wood and 3 lbs of wicker.
Available wood = 3000 board feet
Available wicker = 1400 lbs
Profit margin of A = $35 per unit
Profit margin of B = $42 per unit
Profit margin of C = $20 per unit
To find:
The linear programming problem for given situation.
Solution:
Let the number of units produced of products A, B and C are x, y and z respectively.
Product A Product B Product C Total
Board feet of wood 7 5 4 3000
wicker 4 5 3 1400
Objective function: Maximize
s.t.,
Board feet of wood :
Wicker :
Number of units cannot be negative. So, .
Therefore, the required LPP is
Maximize
s.t.,