An engineer is concerned with the quality of concrete in an old building which is being considered for office use. The concrete strength in the building is classed as s₁, s₂, or s₃, but the class that was used in the old building is unknown. The engineer assigns the strength prior probabilities of 0.3, 0.6 and 0.1 respectively.

The engineer's available actions are:

b1₁: Recommend that all floor slabs with old concrete should be replaced for new concrete at a cost of 10 units.

b2: Restrict the use of the rooms with old concrete to light office use. This will incur no cost unless the concrete has a strength of s₁, in which case the cost of future repairs will be 15 units.

b3: Give permission that the rooms with old concrete can be used for all office-use types. If the concrete has strengths of s₁ and s₂, the cost of future repairs will be 30 and 5 units respectively. If the concrete has a strength of s₃, a benefit of 5 units will be earned.

Answer the following:

a)Using the expected cost criterion, determine the optimal action (4 marks)

Suppose now that the engineer takes an old concrete core and has it tested. The reliability of the test is summarized by the following table:

Test result

Test result P(test result|strength) = P(zklsi) S1 S2 21 indicates strength of s1 0.5 0.2 O z2 indicates strength of s1 0.3 0.6 0.3 za indicates strength of s1 0.2 0.7