Exam 17: Dynamic Programming

Alex takes a troop of boy scouts on a hike one weekend.A corpulent young entrepreneur decides to carry a few extra items to sell to his captive audience.His backpack has room for 13 pounds of provisions beyond the necessary pocketknife and tent.The weights of the most popular snacks are as follows: 12 ounces for item A, 3 ounces for item B, 6 ounces for item C and 16 ounces for item D.His net profit for these items are $1.50 for A, $0.50 for B, $1.00 for C, and $2.50 for D.He scans the pantry at his house before packing his backpack and notes that he has available 24 A's, 16 B's, 12 C's, and 10 D's.Use dynamic programming to determine the maximum possible profits that may be generated.

Dynamic programming can only be used to solve network-based problems.

Discuss, briefly, the role of the transformation function.

Discuss, briefly, the difference between a decision variable and a state variable.

Figure M2.1 -In Figure M2.1, arrow S₁ represents a(n)

The data below is a dynamic programming solution for a shortest route problem. -According to Table M2-2, which gives a solution to a shortest route problem solved with dynamic programming, the total distance from City 1 to City 7 is 14.What is the shortest distance from City 3 to City 7?

There are four items (A, B, C, and D) that are to be shipped by truck. The weights of these are 3, 7, 4, and 5 tons, respectively, and the plane can carry 13 tons. The profits (in thousands of dollars) generated by these are 3 for A, 4 for B, 2 for C, and 5 for D. There are three units of each available for shipment. The maximum possible profit for this would be

The data below details the distances that a delivery service must travel.Use dynamic programming to solve for the shortest route from City 1 to City 8.

There are three items (A, B, and C) that are to be shipped by air. The weights of these are 4, 5, and 3 tons, respectively. The profits (in thousands of dollars) generated by these are 6 for A, 7 for B, and 5 for C. A total of 14 tons may be carried by the plane. There are four units of each available for shipment. What is the maximum possible profit for this situation?

Develop the shortest-route network for the problem below, and determine the minimum distance from node 1 to node 7.

The data below is a dynamic programming solution for a shortest route problem. -Using the data in Table M2-1, determine the optimal arc of stage 2.

The data below is a dynamic programming solution for a shortest route problem. -According to Table M2-2, which gives a solution to a shortest route problem solved with dynamic programming, which cities would be included in the best route?

A transformation changes the identities of the state variables.

For knapsack problems, s_n-1 = a_n × s_n + b_n × d_n + c_n is a typical transformation expression.

What is the decision criterion for a shortest route problem?

There are four items (A, B, C, and D)that are to be shipped by air.The weights of these are 5, 7, 8, and 11 tons, respectively.The profits (in thousands of dollars)generated by these are 5 for A, 8 for B, 7 for C, and 10 for D.There are 3 units of A, 4 unit of B, 6 units of C, and 5 units of D available to be shipped.The maximum weight is 44 tons.Use dynamic programming to determine the maximum possible profits that may be generated.

There are six cities (City 1-City 6) serviced by a particular airline. Limited routes are available, and the distances for each of these routes are presented in the table below. -What is the shortest route between City 1 and City 5?

The following information describes a shortest-route problem with the distance in miles.How many stages will this dynamic problem have?

-Using the data in Table M2-5, determine the optimal distance of stage 1.

-For the shortest route problem described in Table M2-3, what is the distance for the shortest route?