Home › Textile Costing › Lecture 17
Textile Costing · Lecture 17
Optimal Yarn Mix
Allocating 46 frames among six counts to maximise contribution, within the limit of 780 bags of daily shipment.
Product mixConstraintsContribution per frame
The decision
A mill has 46 frames and can ship at most 780 bags a day. Coarser counts earn less per bag but produce many more bags per frame; finer counts the reverse. The frame — the scarce resource — must be given to the count that earns the most per frame, subject to the shipping limit. Change the frames allotted to each count (row 2) and watch the totals; the two constraint rows tell you if the plan is feasible.
| A | B | C | D | E | F | G | H | |
|---|---|---|---|---|---|---|---|---|
| 1 | Count (Ne) | 6 | 8 | 10 | 12 | 16 | 20 | Total / limit |
| 2 | Frames allotted | 36 | ||||||
| 3 | Price (US$/kg) | Rs/$ | ||||||
| 4 | Price per bag (Rs) | 5,445 | 5,581 | 5,717 | 5,853 | 5,989 | 6,261 | |
| 5 | OPS | bags/frame @1 OPS | ||||||
| 6 | Bags per frame per day | 25.65 | 23.40 | 19.80 | 15.30 | 11.97 | 9.27 | |
| 7 | Total bags per day | 153.9 | 140.4 | 118.8 | 91.8 | 71.8 | 55.6 | 632.3 |
| 8 | Variable cost per bag excl. EDS (Rs) | 4,552 | 4,552 | 4,552 | 4,552 | 4,552 | 4,552 | |
| 9 | Export development surcharge 0.25% | 13.61 | 13.95 | 14.29 | 14.63 | 14.97 | 15.65 | |
| 10 | Contribution per bag | 879 | 1,015 | 1,151 | 1,287 | 1,422 | 1,694 | |
| 11 | Contribution per frame per day | 22,553 | 23,752 | 22,786 | 19,685 | 17,026 | 15,703 | |
| 12 | Total contribution per day | 135,317 | 142,510 | 136,716 | 118,108 | 102,154 | 94,215 | 729,021 |
| 13 | Fixed cost per day (46 frames × 14,000) | 644,000 | ||||||
| 14 | Profit per day | 85,021 | ||||||
| 15 | Profit per month | 2,550,616 |
blue = input (edit me)grey = formula (click to see it)
With six frames on every count the mill earns about Rs 85,000 a day. Ne 8 gives the highest contribution per frame (≈23,750), so the optimum pushes frames towards Ne 8 and Ne 6 until the 780-bag shipping limit binds — then the remaining frames go to the finer counts that use less shipping capacity per frame. Try it: the sheet is a hand-driven linear programme.