Problem 1. The North Dakota Snow Bank has 10 million dollars to invest in loans. The types of loans NDSB makes and their annual rates of return and their security ratings are

The NDSB wishes to maximize the return on the money it lends. However, the following restrictions must hold: business loans must equal at least \(40 \%\) of the total amount lended; snowmobile loans must be no more than \(20 \%\) of mortgage loans; the total number of safety points achieved must be at least 62 . (Note: Regarding the security rating, each million dollars lended gets the number of safety points specified above according to the type of loan. For example, if 5 million dollars were invested in snowmobile loans this would yield (5)(2) =10 safety points. If 5 million dollars were invested in mortgage loans, this would yield (5)(8)=40 safety points.) Formulate and solve a linear programming model which would maximize annual return in the face of the restrictions imposed.

#2: Texas Dextrous is attempting to devise a minimum cost meal which meets the government's recommended nutritional standards. Each meal for an adult must contain 100 units of protein, 400 units of carbohydrates, 20 units of minerals, and 50 units of vitamins. Working with dried beans, milk, eggs, ground beef, carrots, and spinach which have the nutritional characteristics as listed below, set up a model which would yield the minimum cost meal. Is your answer reasonable? Please discuss.

#3: Goose Marine produces rowboats, sailboats, and cabin cruisers. The profit for each of these boats is Goose can sell as many sailboats and cabin cruisers as can be produced; however, a maximum of 100 rowboats can be sold. Goose Jealously guards its reputation as being a crafter of both power boats and sailboats, therefore it is specified that the number of sailboats cannot exceed twice the number of cabin cruisers made, and, the number of cabin cruisers cannot exceed twice the number of sailboats made. Set up a linear programming model for the objective of maximizing profits under the circumstances given.

#6. Spencer Farm Machinery produces harvesters in three plants and ships the harvesters to four sales areas. In the table below the values given are the profits (in thousands of dollars) per harvester shipped over the designated route. The profits are affected by both transportation costs and differing manufacturing costs at the four plants. Find the transportation plan that will maximize profits.

Destinations

#10. Consider the network below. Formulate a Solver model and find the shortest path from node 1 to node 9. Note -- flow only occurs in one direction from the smaller node to the larger.

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Deliverable: Word Document