It is possible to create a perfectly fine soap without Shea butter, cocoa butter, or jojoba oil.
The simple blending of olive oil, coconut and soybean oils produced the suds you see on the left. Let's not sneer at the common little soy legume! Soy bean oil produces a gently cleansing salt that gives a boost to bubbles and acts as a humectant. It's only drawback is that it does not give a satisfying hardness to the bar, so it must be balanced by other oils that do harden nicely when saponified, such as coconut and olive.
I took this humble blend of oils and added some super mineral sources from earth and sea: Dead sea salt, dulse and nori, bentonite clay, French green clay, mined sodium chloride, ground patchouli, and activated charcoal give this one some super mineralised cleansing properties. It wouldn't be complete without a scent of clean earthiness, so I combined patchouli, peppermint, cypress, basil and rosemary for the perfect complement. This soap is full of interesting ingredients and strong cleansing power, yet friendly to the budget. When the loaf has hardened and is ready to cut, I plan to offer generous large long lasting bars that weigh over 5 oz each for no more than $4.