A large farm is trying to decide how to reduce the spread of a virus that is spreading contagiously among its animals.

They have allocated a budget of $200,000 to take measures against the virus, and they are considering the following two kinds of interventions.

(i) The pathogen only spreads between animals that are close together. Their current plan for the animals has each animal coming in contact with 30 others. The farm could instead organize the layout of its operations to have fewer animals come in contact with each other; this would be more expensive, since it would use more space, but if they spend x dollars, they can use enough space that each animal comes in contact with only

30 - (x / 10,000)

others

(ii) Currently, any infected animal has a .07 probability of infecting each other animal it comes in contact with. The farm could install machines that emit ultraviolet light to reduce the amount of virus in the air; the more money they spend on this, the more of these machine they can install. If they spend y dollars, they can install enough machines to reduce the probability that each infected animal spreads the virus to each animal it comes in contact with; the new probability, if they spend y dollars, would be

.07 - (y / 10,000)

The farm is currently unsure how to divide its budget of $200,000 among these two interventions, so theyre planning to spend equally on the two of them: $100,000 on each.

They ask you whether you think this is the right plan, or whether they should do some- thing different. If you think theyre doing the right thing, explain why. If you think theres a better way they could divide the budget between these two options, then describe a different way of dividing the budget, and explain why you think this different allocation of the budget would be a better idea than their current plan.