Calculating Available Work Days

An economist models a consumer's choices between goods A and B using the preference representation U(A, B) = A^0.5 * B^0.5. A second economist models the same consumer's choices using the representation U(A, B) = 2A + 3B. Both economists correctly apply the same optimization principles to find the consumer's optimal consumption bundle given a budget. They arrive at different mathematical expressions for the optimal quantities of A and B. Which statement best explains why their final expressions are different?

A consultant is modeling their time allocation for a project with a total duration of 90 days. If this consultant decides to increase their amount of free time from 20 days to 30 days, the total number of days available for work will consequently decrease by 10.

An independent contractor is hired for a project with a total duration of 180 days. If the contractor plans to take 35 days of free time, they will have ____ days available for work.

An analyst compares the time allocation of two consultants. Consultant A has a contract for a 90-day period and takes 30 days of free time. Consultant B has a contract for a 75-day period and takes 15 days of free time. Both consultants end up working the exact same number of days. Which statement best analyzes why this is the case?

Evaluating Contract Options

An economist is modeling the time allocation for four different individuals over a fixed period. For each individual's scenario, match the total available time and the chosen amount of free time with the correct resulting number of work days.

Relationship Between Free Time and Work Time

A project manager needs to ensure a team completes at least 45 days of work on an initiative. They are considering two potential timelines: a 60-day total period or a 75-day total period. Which statement best evaluates the two options based on the maximum amount of free time the team could take while still meeting the work requirement?

Analyzing Changes in Time Allocation