| Let: | A = # of units of A produced |
| B = # of units of B produced | |
| C = # of units of C produced | |
| D = # of units of D produced |
|
Max Z =
|
40 A + 36 B + 24 C + 48 D |
| s.t. |
2 A +
|
B +
|
2.5 C +
|
5 D
|
<
|
1,200
|
|
A +
|
3B +
|
3.5 C +
|
<
|
1,300
|
||
|
A
|
<
|
120
|
||||
|
C
|
<
|
96
|
||||
|
D
|
>
|
100
|
|
where:
|
A, B, C, D > 0 |
| Let: | S = $ invested in Signature loans |
| F = $ invested in Furniture loans | |
| A = $ invested in Automobile loans | |
| M1 = $ invested in First Mortgage loans | |
| M2 = $ invested in Second Mortgage loans |
|
Max Z =
|
0.18 S + 0.16 F + 0.11 A + 0.09 M1 + 0.1 M2 |
| s.t. |
S
|
|
0.1 (S + F +A + M1 + M2) |
|
S + F
|
|
0.2 (S + F +A + M1 + M2) | |
|
M1
|
|
0.4 (M1 + M2) | |
|
M1
|
|
0.2 (S + F +A + M1 + M2) | |
|
M2
|
|
0.25 (S + F +A + M1 + M2) | |
|
S + F +A + M1 + M2
|
|
1,500,000 |
|
where:
|
S, F, A, M1, M2 > 0 |
| Let: | S = # of Sofas purchased |
| B = # of Beds purchased | |
| D = # of Dining Sets purchased | |
| C = # of Chests purchased | |
| P = # of Patio Sets purchased |
|
Max Z =
|
50 S + 20 B + 75 D + 10 C + 25 P |
| s.t. |
45 S +
|
60 B +
|
75 D +
|
15 C +
|
95 P
|
<
|
500
|
|
S
|
<
|
B | |||||
|
P
|
<
|
S | |||||
|
P
|
<
|
B | |||||
|
P
|
<
|
D | |||||
|
P
|
<
|
C | |||||
|
45 S +
|
25 B +
|
35 D +
|
5 C +
|
30 P
|
<
|
450
|
|
where:
|
S, B, D, C, P > 0 |
| Let: | R1 = $ spent on Radio advertising in the first half of the year |
| R2 = $ spent on Radio advertising in the second half of the year | |
| T1 = $ spent on Television advertising in the first half of the year | |
| T2 = $ spent on Television advertising in the second half of the year | |
| N1 = $ spent on Newspaper advertising in the first half of the year | |
| N2 = $ spent on Newspaper advertising in the second half of the year | |
| M1 = $ spent on Magazine advertising in the first half of the year | |
| M2 = $ spent on Magazine advertising in the second half of the year |
|
Max Z =
|
5 (R1 + R2) + 20 (T1 + T2) + 10 (N1 + N2) + 15 (M1 + M2) |
| s.t. |
R1 + R2 + T1 + T2 + N1 + N2 + M1 + M2
|
|
2,000,000
|
|
R1 + T1 + N1 + M1
|
|
1,100,000
|
|
|
N1 + M1
|
|
200,000
|
|
|
N2 + M2
|
|
200,000
|
|
|
T1
|
|
0.8 (R1 + T1 + N1 + M1) | |
|
T2
|
|
0.8 (R2 + T2 + N2 + M2) | |
|
R1 + R2
|
|
50,000
|
|
|
T2
|
|
0.25 (T1 + T2) |
|
where:
|
R1, R2, T1, T2, N1, N2, M1, M2 > 0 |
| Let: | F = # of fancy lamps produced |
| O = # of ornate lamps produced | |
| P = # of plain lamps produced | |
| R = # of rococo lamps produced |
|
Max Z =
|
100 F + 150 O + 200 P + 200 R |
| s.t. |
10 F +
|
8 O +
|
10 P +
|
20 R
|
<
|
1,000
|
|
2 F +
|
3 O +
|
1 P +
|
1 R
|
<
|
200
|
|
|
10 F +
|
20 O +
|
15 P +
|
30 R
|
<
|
5,000
|
|
|
1 P -
|
2 R
|
>
|
0
|
|
where:
|
F, O, P, R > 0 |
| Let: | P = # of bottles of El Presidente produced |
| C = # of bottles of Canario produced |
|
Max Z =
|
2 P + 2.5 C |
| s.t. |
3 P +
|
4 C
|
<
|
20,000
|
|
0.8 P +
|
0.605 C
|
<
|
4,000
|
|
where:
|
P, C > 0 |
| P = | 2,815.884 |
| C = | 2,888.087 |
| Max Z = | 12,851.99 |
