This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
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Let's figure out how to stake your money to minimize your loss by ensuring the same return regardless of which outcome wins.
Step 1: Define the variables. Let S₁ be the amount staked on the outcome with odds 3.50. Let S₂ be the amount staked on the outcome with odds 1.33. The total stake is 5000. So, S₁ + S₂ = 5000.
Step 2: Set up the condition for equal returns. To minimize loss, we want the payout to be the same no matter which outcome wins. Payout if outcome 1 wins = S₁ × 3.50 Payout if outcome 2 wins = S₂ × 1.33 We set these equal: S₁ × 3.50 = S₂ × 1.33
Step 3: Solve the system of equations. From S₁ + S₂ = 5000, we can express S₂ as S₂ = 5000 - S₁. Substitute this into the equal returns equation: S₁ × 3.50 = (5000 - S₁) × 1.33 3.50 S₁ = 5000 × 1.33 - 1.33 S₁ 3.50 S₁ = 6650 - 1.33 S₁ Add 1.33 S₁ to both sides: 3.50 S₁ + 1.33 S₁ = 6650 4.83 S₁ = 6650 S₁ = 6650 / 4.83 S₁ ≈ 1376.81
Now find S₂: S₂ = 5000 - S₁ S₂ = 5000 - 1376.81 S₂ ≈ 3623.19
Step 4: Calculate the potential return and the loss. If outcome 1 wins: Return = 1376.81 × 3.50 = 4818.835 If outcome 2 wins: Return = 3623.19 × 1.33 = 4818.8427 The return is approximately 4818.84.
The total money staked is 5000. The loss will be 5000 - 4818.84 = 181.16.
To have the smallest loss, you should stake: S₁ = 1376.81 on the outcome with odds 3.50. S₂ = 3623.19 on the outcome with odds 1.33. This strategy results in a loss of approximately 181.16 regardless of which outcome wins.
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Define the variables. Let S₁ be the amount staked on the outcome with odds 3.50.
This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.