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In: Operations Management

A swim club is designing a new pool to replace its old pool. The new pool...

A swim club is designing a new pool to replace its old pool. The new pool would need to last for 10 years since the club is planning on relocating after 10 years. A concrete shell would cost $85,000 and last for all 10 years. Another option is to install a vinyl liner that would cost only $70,000 to install. However, the vinyl is not guaranteed to last for all 10 years, and it has a 40% chance of breaking down. Repair of the vinyl would cost $40,000 and would extend the life of the vinyl liner to the 10-year mark. If both options are acceptable to the swim club, which one minimizes cost?

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Expert Solution

The concrete cell has no additional cost in the life span of 10 years. The only cost is the installation cost which is $85000.

The swim club also has the option to install a vinyl liner which has an installation cost of $70000. This vinyl liner has a 40% chance of breaking down before 10 years and a 60% chance that it will not breakdown and last for 10 years. If it breaks, then the repair cost is $40000.

The expected additional cost for the vinyl liner if it breaks down = $40000 * 0.4 = $16000

The expected additional cost for the vinyl liner if it does not breakdown = 0 * 0.6 = 0

The total expected additional cost of the vinyl liner = $16000

The total expected cost = $70000 + $16000 = $86000

The minimum cost is $85000 which is of the concrete shell. The swim club should opt for the concrete shell.

keosha answered 2 months ago
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