The Cheapest Cotton and Linen Blend That Meets a Stated Yarn Strength: An Interaction Model and Its Answer

Blending cotton with linen is usually discussed in the language of character: hand, lustre, drape, coolness. Those are real, but a producer buying fibre by the kilogram and selling yarn against a strength specification needs the blend discussed in arithmetic as well. How much linen, at several times cotton's price, must actually be bought to lift a cotton yarn to a stated tenacity? This paper answers with a stated blend model that includes an interaction term, applies a stated spinning efficiency, and finds the cheapest blend meeting a stated warp tenacity target under a stated hand-feel ceiling on linen content. In the computed results, the best linen fraction is 0.45; the best tenacity is 19.04; the best cost usd per kg is 4.11; the cotton only tenacity is 13.2; the half blend tenacity is 19.62. Buy linen against the strength specification, not against a customary recipe fraction. The study is simulated, not measured; all inputs are stated assumptions, printed in the accompanying computation, which readers may replace with their own values and re-run.