12  Answers

Exercise 1.6: Intro to Linear Functions

1) Answers will vary

3) Answers will vary

5) \(f(x)=-2x+10\)

7) a) \(N(m)=15m+200\); b) 380 songs after 12 months

Exercise 2.6: Rate of Change

1) a) \(P=90t+2000\); b) \(P=2t+2000\)

3) Undefined; \(x=2\)

5) \(y=2x+3\)

7) \(y=2x+3\)

Exercise 3.4: LF Applications

1) a) $6.33; b) $14.67; c) $10.5; d) 144 units; e) 264 units; f) 384 units

3) a) \(d(p)=9.2-1.2p\)

5) a) \(C(x)=11.38x+349,500\); b) $399,511.38

7) a) \(R(x)=1.5x\); b) (20,30); c) 1,020; d) $2,480

Exercise 4.4: LP - Geometric Method

1) a) \(6x+4y\leq300\); b) \(30x+72y\leq420\); c) \(12x+10y\leq640\); \(4x+3y\leq480\)

3) a) (2,4) Yes; (10,6) No.; b) (2,4) Yes; (10,6) No.; c) (2,4) No; (10,6) No.

5) a) (0,0); (3,0); (0,6) and (4,5)
(b) (0,6) and (4,5); profit is $48.

7) 28.

9) 2 batches grade A and 5 grade B; 3.6 batches of A and 1 batch of B.

11) 7 chairs and 16 tables.

Exercise 6.4: Transportation Problem

1) Answers will vary.

3) a) $23; b) \(\text{Indicator}_{(II,1)}= -13\), \(\text{Indicator}_{(I,2)}= 4\) ; c) No! (II,1) has negative indicator value. d) $10

5) a) Ship 1 unit via \((I,1)\), 2 via \((I,2)\), 2 via \((I,3)\), 4 via \((II,3)\) and 1 via \((III,3)\);
c) \(\text{Indicator}_{(II,1)}= 5\); \(\text{Indicator}_{(II,1)}= -4\) b) $37. d) No; $33.