A scooter can travel between 22 and 28 miles on each galon of gasoline. If one gallon costs between 3.75 and 3.95per gallon abou
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<h3>Answer:</h3>
- x-intercept: 82.75
- y-intercept: -2.15
To find the x-intercept, set y=0 and solve.
... 0 = log(12x +7) -3
... 3 = log(12x +7) . . . . add 3
... 1000 = 12x +7 . . . . take the antilog. (10^3 = 1000)
... 993 = 12x . . . . . . . .subtract 7
... 82.75 = x . . . . . . . . divide by 12
To find the y-intercept, set x=0 and solve.
... y = log(12·0 +7) -3
... y = log(7) -3 . . . . . . simplify
... y ≈ 0.85 -3 = -2.15 . . . . use a calculator for the log function
Answer:
- A: $37500
- B: $17500
Step-by-step explanation:
Natsano can satisfy his constraints by investing the first $20,000 in Company A, then splitting the remaining $35,000 evenly between the companies. For best return, he needs to invest as much as possible in Company B, but each such dollar (after the first 20k) must be matched by a dollar invested in Company A. That is, his investments should be ...
- Company A: $37,500
- Company B: $17,500
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The attached graph shows the feasible region of investments (doubly shaded). The vertex that maximizes the objective function (return on investment) is the one highlighted. (It puts the objective function line as far as possible from the origin.)
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Sometimes graphing the constraints is more work than necessary if there is some simple logic that quickly identifies the solution.
