Quantity analysis

Consider the following matrices:

1. (worth 1 point) What is element b2,1? ______

2. (worth 1 point) Find BT, the transpose of B.

3. (worth 1 point) Write the identity matrix that is the same order as C.

4. (worth 3 points) Perform the matrix multiplication BxC. Show work, as I did during the video lesson.

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5. (worth 5 points) Solve the system of linear equations. Use the Gauss-Jordan Elimination method. Show every step and indicate each operation within each step, as I did during the lesson.

6. (worth 4 points) An investment of $88,000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned​ 8% interest, the second​ 6%, and the third​ 9%. Total interest from the investments was $6660. The interest from the first investment was 3 times the interest from the second. Set up the system of linear equations to solve this problem but DO NOT solve.

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7. Chocolate Heaven produces two kinds of chocolate bars. A bar of the gourmet version is made of two cups of sugar and three cups of cocoa. A bar of the version that is marketed to children is made of one cup of sugar and one cup of cocoa. Chocolate Heaven makes a profit of $1.25 from each bar of the gourmet version and a profit of $1.00 from the children’s version. If they are limited to 154 cups of sugar and 198 cups of cocoa per day then how many of each version must the company make per day to maximize their profits?

Each part is worth 1 point.

a) Write out the objective equation and constraints.

b) Graph the constraints.

c) Find the all vertices of the feasible region.

d) Find the vertex that maximizes profits.

e) Write the answer in a complete sentence.