ABSF Chemical Coatings Inc. is a chemical plant that produces highly volatile varnishes for the furniture industry. The plant is located adjacent to a small residential area. The probability of an explosion at ABSF Chemical Coatings Inc. is a function of how much it invests in safety equipment as given in the following table. If an explosion were to occur, the loss to society (damaged equipment, death of employees, etc.) is expected to be $100 million. Find the optimal level of safety from societal perspective.
| Safety Expenditure (millions of $) | Probability of Loss |
| $0.0 | 0.0500 |
| 0.25 | 0.0450 |
| 0.50 | 0.0410 |
| 0.75 | 0.0385 |
| 1.00 | 0.0364 |
| 1.25 | 0.0355 |
Suppose that ABSF Chemical Coatings Inc. only has to pay one-half of the losses that occur. How much should ABSF spend on safety?