stat MATH 106

(5 pts) Determine how many five-character codes can be formed if the first, second, and third characters are letters, the fourth character is a nonzero digit, the fifth character is an odd digit, and repetition of letters and digits are allowed.1. ______ A.92B.3,510C.312,000D.790,920   (5 pts)3. _______ A. 5B. 25C. 120D.3,125    (10 pts) A stamp collector has a set of five different stamps of different values and wants to take a picture of each possible subset of his collection (including the “empty set,” depicting just the picture frame!), i.e., pictures showing no stamps, one stamp, two stamps, three stamps, four stamps, or five stamps. In each picture showing two or more stamps, the stamps are in a row. , determine the maximum number of different pictures possible, when the difference between two pictures would be either in the number of stamps or in the horizontal order of the stamps. For example, if the stamp collector had just two different stamps (say A and B) of different values, he would have five pictures showing: A, B, AB, BA, and the empty frame.          Let = {10, 20, 30, 40, 50, 60, 70, 80, 90}, = {30, 50, 60, 90} and = {10, 20, 50, 80, 90}.List the elements of the indicated sets. (No work/explanation required).         (9 pts) Use the given information to complete the following table.n(U) = 80 , n(A) = 22,n(B) = 35,n(A B) = 15.(No work/explanation required)                  (20 pts) Two kinds of cargo, A and B, are to be shipped by a truck. Each crate of cargo A is 25 cubic feet in volume and weighs 100 pounds, whereas each crate of cargo B is 40 cubic feet in volume and weighs 120 pounds. The shipping company collects $180 per crate for cargo A and $220 per crate for cargo B. The truck has a maximum load limit of 1,200 cubic feet and 4,200 pounds. The shipping company would like to earn the highest revenue possible.  Fill in the chart below as appropriate. Let be the number of crates of cargo A and the number of crates of cargo B shipped by one truck.  State an expression for the total revenue earned from shipping crates of cargo A and crates of cargo B.   Using the chart in (a), state two inequalities that and must satisfy because of the truck’s load limits.      State two inequalities that and must satisfy because they cannot be negative.     State the linear programming problem which corresponds to the situation described.   Solve the linear programming problem. You will need to find the feasible region and determine the corner points. You do have to submit your graph, and you do have to show algebraic work in finding the corner points, but you must list the corner points of the feasible region and the corresponding values of the objective function.      Write your conclusion with regard to the word problem. State should be shipped in the truck, in order to earn the highest total revenue possible. State the value of that .  

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