Mango Fresh Company is a company engaged in the production of beverages from mangoes. There are...
Homework Answers
Let Sj and Nj be the kgs of super mango and standard mango mixed to form the drink-j where j=p, q, k
Maximize Z = (20 - 7) * (Sp + Np) + (30 - 10) * (Sq + Nq) + (50 - 20) * (Sk + Nk)
Subject to,
Sp + Sq + Sk <= 5000
Np + Nq + Nk <= 10000
10 Sp + 5 Np >= 6 (Sp + Np) or, 4 Sp - 1 Np >= 0
10 Sq + 5 Nq >= 8 (Sq + Nq) or, 2 Sq - 3 Nq >= 0
10 Sk + 5 Nk >= 9 (Sk + Nk) or, 1 Sk - 4 Nk >= 0
Sj, Nj >= 0 for j=p, q, k
-----------------------------------------------------------
Excel formulation
Solution
| Sp | Np | Sq | Nq | Sk | Nk | ||||
| Kgs. | 2333 | 9333 | 0 | 0 | 2667 | 667 | |||
| Revenue | 20 | 20 | 30 | 30 | 50 | 50 | |||
| Cost | 7 | 7 | 10 | 10 | 20 | 20 | |||
| Profit | 13 | 13 | 20 | 20 | 30 | 30 | 251,667 | ||
| s.t. | |||||||||
| Capacity super mango | 1 | 1 | 1 | 5000 | <= | 5000 | |||
| Capacity std. mango | 1 | 1 | 1 | 10000 | <= | 10000 | |||
| Quality Prince | 4 | -1 | 0 | >= | 0 | ||||
| Quality Queen | 2 | -3 | 0 | >= | 0 | ||||
| Quality King | 1 | -4 | 0 | >= | 0 |
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