A construction firm places bids on various portions of the work in building a new office tower. The key bids it submits are for electrical work and for plumbing. The bid for the electrical work estimates 64 weeks of labor (e.g., 1 electrician for 64 weeks or 8 for 8 weeks). The bid for the plumbing estimates 120 weeks of labor. Standard procedures indicate that the standard deviations for these estimates are 6 weeks for electrical work and 15 weeks for plumbing.
(a) Find the expected number of weeks of labor provided by the company if it wins both bids.
(b) Would you expect to find positive, negative, or no correlation between the numbers of weeks of the two types of labor needed for the construction?
(c) Find the standard deviation of the total number of weeks of work if the correlation between the weeks of labor for electrical work and plumbing is ρ = 0.7.
(d) What is the effect of the dependence between the number of weeks of electrical and plumbing labor? In particular, when preparing bids, would the firm prefer more or less dependence?
(e) The firm earns a profit of $200 per week of electrical work and a profit of $300 per week of plumbing work. What are the expected profits from this contract and the standard deviation of those profits? Assume ρ = 0.7 as in part (c).
(f) Do you think that the firm will make more than $60,000 on this contract?