Question: Question 1: A camper is considering taking two types of items on a camping trip. Item 1 weighs a₁ lb, and item 2 weighs a₂ lb. Each type 1 item ears the camper a benefit of c₁ units, and each type 2 item earns the camper a benefit of c₂ units. The knapsack can hold items weighing at most b lb.

a. Assuming that the camper can carry a fractional number of items along on the trip, formulate an LP to maximize benefit.

b. Show that if c₂ / a₂ \(\ge \) c₁ /a₁, then the camper can maximize benefit by filling a knapsack with b/a₂ type 2 items.

c. Which of the linear programming assumptions are violated by this formulation of the camper's problem?