Exam 4: Graphing and Optimization

Solve the problem. -An economy is based on two sectors, agriculture and manufacturing. Production of a dollar's worth of agriculture requires an input of $0.40 from agriculture and $0.10 from manufacturing. Production of a dollar's worth of manufacturing requires an input of $0.20 from agriculture and $0.30 from manufacturing. Find the output for each sector that is needed to satisfy a final demand of $16 billion for agriculture and $32 billion for manufacturing.

Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM. -A A $ 000 tru trst is to be invested in bonds paying 9%, CDs paying 8%, and mortgages paying 10%. The sum of the amount invested in bonds and the amount invested in CDs must equal the mortgage investment. To earn an $11,400 Annual income from the investments, how much should the bank invest in each? Let x represent the amount invested in bonds, y the amount invested in CDs, and z the amount invested in mortgages.

Solve the system mentally, without the use of a calculator or pencil-and-paper calculation. Try to visualize the graphs of both lines. -

Solve using Gauss-Jordan elimination. -2

Solve the system of equations by substitution. -

Provide an appropriate response. -Given the matrix B: What is the size of B?

Solve the system of equations by graphing. -Use a graphing utility to solve the system . Give the . Give theanswer to three decimal places.

Solve the problem. -A chemistry department wants to make 3 liters of a 17.5% basic solution by mixing a 20% solution with a 15% solution. How many liters of each type of basic solution should be used to produce the 17.5% solution?

Use the given encoding matrix A to solve the problem. -The following message was encoded with matrix . Decode this message . Decode this message.

Write the word or phrase that best completes each statement or answers the question. -

Solve the system of equations by substitution. -

Find the inverse, if it exists, of the given matrix. -

Solve the problem. -A hospital dietitian wants to insure that a certain meal consisting of rice, broccoli, and fish contains exactly 26,800 units of vitamin A, 840 units of vitamin E, and 11,160 units of vitamin C. One ounce of rice contains 400 units of vitamin A, 20 units of vitamin E, and 180 units of vitamin C. One ounce of broccoli contains 800 units of vitamin A, 60 units of vitamin E, and 540 units of vitamin C. And one ounce of fish contains 2,400 units of vitamin A, 40 units of vitamin E, and 810 units of vitamin C. How many ounces of each food should this meal include? Set up a system of linear equations and solve using Gauss-Jordan elimination.

Provide an appropriate response. -Write the augmented matrix for the system.

Solve the system as matrix equations using inverses. -

Provide an appropriate response. -Given matrix A: What is the size of A?

Solve the system of equations by graphing. -

Provide an appropriate response. -Given A = , determine determinewhich of the following products is NOT defined.

Solve the problem. -The input-output matrix for an economy is Find the production matrix X.

State whether the matrix is in reduced form or not in reduced form. -