Question: 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 on 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 x1 floors of plan A, x2 floors of plan B, and x3 floors of plan C.
a. What interpretation can be given to the vector
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. [M] 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.