Question 10. Francis has $100,000 to invest and decides to using stocks, bonds, and money markets. The stocks earn 12% per year, the bonds earn 8% per year, and the money market investment bring in 4% annually. Francis needs to realize $10,000 each year from the three investments. The amount invested in the money market venture is the same as the sum of twenty percent of the stock investment and ten percent of the bond investment. (a) Define your variables and set up the system of (b) Set up the augmented matrix for the system. linear equations. ALLOF (d) 1 0 -11 -100, 000 (c) Given that the final step in the Echelon method is given by 0 1 12 200, 000 , how much should 0 01 15, 000 Francis invest in stocks, bonds, and the money market account? -1 0 HN Question 11. Consider matrix A = 0 1 , which has inverse A-1 = CO ColtCOIN HOO -2 0 2x - y = 4 Use A- to solve the system { x + z = 2 x - 2y = 3Question 13. The Mundo Candy Company makes three types of chocolate candy: Cheery Cherry, Mucho Mocha and Almond Delight. The company produces its products in San Diego, Mexico City, and Managua using two main ingredients: chocolate and sugar. (a) Each kilogram of Cheery Cherry requires 0.5 kg (b) The cost of 1 kg of sugar is $4 in San Diego, $2 in of sugar and 0.2 kg of chocolate; each kilogram Mexico City, and $1 in Managua. The cost of 1 kg of Mucho Mocha requires 0.4 kg of sugar and 0.3 kg of chocolate is $3 in San Diego, $5 in Mexico City, of chocolate; and each kilogram of Almond Delight and $7 in Managua. Put this information into a ma- requires 0.3 kg of sugar and 0.3 kg of chocolate. Put trix called C in such a way that when you multiply this information into a 2 x 3 matrix called A, labeling it with matrix A, you get a matrix representing the the rows and columns. ingredient cost of producing each type of candy. (c) Only one of the two products AC and CA is meaningful. Determine which one it is, calculate (d) From your answer to part (c), what is the combined the product, and describe what the entries represent. Mocha in Managua? sugar-and-chocolate cost to produce 1 kg of Mucho (e) Mundo Candy needs to quickly produce a special shipment of 1000 kg of Cheery Cherry, 200 kg of Mucho Mocha, and 500 kg of Almond Delight, and it decides to select one factory to fill the entire order. Use is the smallest. matrix multiplication to determine in which city the total sugar-and-chocolate cost to produce the order