A large apartment building is to be built using modular construction techniques. The arrangement of apartments on any particular floor is to be chosen from one of three basic floor plans. Plan A has 18 apartments one one floor, including 3 three- bedroom units, 7 two-bedroom units, and 8 one-bedroom units. Each floor of plan B includes 4 three-bedroom units, 4 two-bedroom units, and 8 one-bedroom units. Each floor of plan C includes 5 three-bedroom units, 3 two-bedroom units and 9 one-bedroom units, Suppose the building contains a total of x, floors of plan A, x2 floors of plan B, and floors of plan C. a) What interpretation can be given to the vector x, 7? b) Write a formal linear combination of vectors that expresses the total numbers of three-, two-, and one-bedroom apartments contained in the building. c) Is it possible to design the building with exactly 66 three-bedroom units, 74 two-bedroom units, and 136 one-bedroom units? If so, is there more than one way to do it? Explain your answer.

Hello Dolly, Inc. crafts three styles of dolls: Lexi, Maysy, and Dizzy. Each doll requires sewing time, painting time, and supplies. Sewing machines are available for only 118 hours, only 2805 hours are available for painting, and 390.5 lbs. of supplies are available. Each Lexi doll requires 0.2 hours of sewing, 9 hours of painting, and 0.7 lbs. of supplies. Each Maysy doll requires 0.4 hours of sewing, 10 hours of painting, and uses 0.9 pounds of supplies. Each Dizzy doll requires 0.5 hours of sewing, 7 hours of painting, and 2 pounds of supplies. If the company earns a profit of $145 per Lexi doll, $155 per Maysy doll, and $150 per Dizzy doll, how many of each doll should the company produce to maximize profit? How much profit will result? (Use for the number of Lexi dolls, y for the number of Maysy dolls, and z for the number of Dizzy dolls.) Maximize P = subject to ≤118 ≤2805 <390.5 Enter the solution to the simplex matrix below. If there is no solution enter 'DNE' in the boxes…

Find 11 (3 (3x + 2y)dA where R is the parallelogram with vertices (0,0), (4,5), (-3,1), and (1,6). Use the transformation = 4u - 3v, y = 5u + v.

A real estate investment trust​ (REIT) owns​ first-class office properties in selected markets. According to its​ website, the occupancy rates last year for its holdings in four major cities are available below. Complete parts a through c below.