# MATH 2307 Linear Algebra Spring 2019 Application Project 2: Linear Economic Models By Prof. César Garza Due Tuesday, February 5 at 4:00 p.m.: First read very carefully the file Linear Economic Models Theory. pdf attached to this homework . Read the explanations and the fully worked examples presented there. Then submit your full solutions to the following problems in person at the beginning of class or online in Blackboard before the deadline. You are encouraged to use Python, Mathematica, Julia, etc. to verify your answers, but include all the steps you took in your submission Problem 1: Suppose the coal and steel industries form a closed economy. Every \$1 produced by the coal industry requires \$0.30 of coal and S\$0.70 of steel. Every \$1 produced by steel requires S0.80 of coal and \$0.20 of steel. Find the annual production (output) of coal and steel if the total annual production is \$20 million. (Hints: The last sentence implies another linear equation) Problem 2: A painter, a plumber and an electrician enter into a cooperative arrangement in which each of them agrees to work for himself/herself and the other two for a total of 10 hours per week according to the schedule shown in Table 2.8. For tax purposes, each person must establish a value for his/her services. They agree to do this so that they each come out even -that is, so that the total amount paid out by each person equals the amount he/she receives. What hourly rate should each person charge if the rates are all whole numbers between \$30 and \$60 per hour? Table 2.8 Supplier Painter Plumber Electrician Painter 2 Consumer Plumber 4 Electrician 4 4 i 2 ints: First convert the values in the table into percentages -out of the 10 hours- in decima m. For the matrices, you may want to multiply by a factor to get rid of decimals and rk with integers. Your row-reduced echelon matrix should contain fractions. Keep the

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