MATH 163 A. ASSIGNMENT #4 Solve for u, x, y and z in the matrix equation. x 2 2 3 z 10 1 1. 4 2 y 3 0 3 4 u B. 1 1 3 Given B = A = 4 1 2 0 1. AB C. 4. 3 A 2C T 2 5 1 3 2. 2 3 4 0 0 1 1 2 1 Solve the system of equations using the inverse of the coefficient matrix. 1. E. 2 1 2 and C = , calculate: 3 2 4 3. BC 2. BA 2 4 u 2 2 0 1 2 z 1 4 4 Determine the inverse matrix of the following matrices, if they exist. 1. D. 2 3 1 1 2 y 1 2. 3 4 3 1 x 1 4 2x 5 y 3 x 3y 2 2. x 4y z 3 2x 3y 2z 1 x 2 y 3z 7 Applications 1. The Theatre charges $4 for children and $8 for adults. One weekend, 900 people attended The Theatre, and the admission receipts totaled $5840. This is represented by the following matrix equation where x is the number of children and y is the number of adults. 1 1 x 900 4 8 y 5840 (a) Find the number of children and adults attending. (b) If the total attendance is 1000 and the admission receipts total $6260, find the number of children and adults attending. MATH 163 ASSIGNMENT #5 Linear Programming 1. 2. Minimize P 15 x 8 y Subject to x 2 y 20 3 x 2 y 36 x0 y0 The National Business Machines Corporation manufactures two models of fax Machines: A and B. Each model A costs $200 to make, and each model B costs $300. The profits are $25 for each model A and $40 for each model B fax machine The total number of fax machines demanded per month does not exceed 2500. The company has earmarked no more than $600,000 per month for manufacturing costs. Calculate the number of units of each model that should be produced to maximize the monthly profits. 3. Madison Finance has a total of $20 million earmarked for Homeowner Loans and Auto Loans. On the average, Homeowner Loans have a 10% annual rate of return, whereas Auto Loans have a 12% annual rate of return. Management has stipulated that the total amount of Homeowner Loans should be greater than or equal to four times the total of Auto loans. Determine the total amount of loans of each type Madison should extend to each category in order to maximize its returns. 4. Technics manufactures two products, television sets and DVD players. The television sets require two hours of labour and $100 of materials per unit. The DVD players require three hours of labour and $50 of materials per unit. The company can afford to spend $1000 each week for the cost of material. An employee can work for a maximum of 40 hours per week. The company makes a profit of $300 for each television set and $150 for each DVD player. Determine the number of television sets and/or DVD players should be made by each employee in order to maximize the company's profit