I only need help solving task c)

Exercise 2. A residential building block is to be constructed where each floor can have one of three possible floor plans A, B or C. Alternative A has 2 one-bedroom apartments, 3 two- bedroom apartments and 9 three-bedroom apartments. Alternative B has 6 two-bedroom apartments and no one-bedroom apartments. Alternative C has 4 one-bedroom apartments, 3 two-bedroom apartments and 7 three-bedroom apartments. Let z{, x5 3 be the number of floors with respectively floor plans A, B and C. 2 (a) Give an interpretation of the vector z; 3 9 (b) Set up a linear combination of vectors that describe the number of one-, two-, and three- bedroom apartments in the building. (c) Is it possible to realize the construction with exactly 34 one-bedroom apartments, 33 two- bedroom apartments and 55 three-bedroom apartments? Are there multiple ways to do this? (d) Does the answer to (c) change if in addition it is required that the building has a maximum of 9 floors? A R, = 2 x + 3y + 92 Rx2 = 6* + Gy + Oz C Rus = 4x+ 3y + /2