Corner Solution

A farmer is deciding how many hours per day to spend on leisure (t), where the possible range is 0 ≤ t ≤ 16. The remaining hours are spent working to produce grain. For any choice of t within this range, the farmer's marginal rate of substitution (the amount of grain they are willing to give up for an extra hour of leisure) is always greater than their marginal rate of transformation (the amount of grain they would actually lose by taking an extra hour of leisure). Given this information, what is the farmer's optimal number of leisure hours?

Profit-Maximizing Advertising Budget

Profit-Maximizing Advertising Budget

Optimal Allocation Decision

A firm is choosing its level of production, q, which can be any value between 0 and 100 units. For any level of production in this range, the marginal revenue gained from selling one more unit is always less than the marginal cost of producing it. Based on this, the firm's profit-maximizing strategy is to find the production level within the 0-100 range where the difference between marginal cost and marginal revenue is smallest.

Optimal Allocation without a Tangency Point

Optimal Study Time Allocation

Analyzing an Optimization Problem with a Boundary Solution

Optimal Time Allocation without an Interior Solution

An individual is deciding on an amount of an activity (x) to undertake, where the feasible range is 0 ≤ x ≤ 100. For each scenario below describing the relationship between the marginal benefit (MB) and marginal cost (MC) of the activity, match it to the optimal choice of x that maximizes net benefit. Assume that for x > 0, MB is a decreasing function of x and MC is an increasing function of x.