i mean even basic differentiation is useful for optimization problems.
Calculus is a shared language in the grand universal ocean of intellectual cultural. Rejecting calculus is rejecting part of that culture…
You need calculus to design a windmill or an auto engine or an electric motor beyond the "just sort of works" level. Most of analog electrical engineering is defined by calculus. Althogh, yes, you can get LTSPICE to do most of that for you.
(A small wind turbine is like a propeller in reverse. A large wind turbine is not, because wind speed varies across the blade circle enough that those stresses dominate the design. It took decades to debug this, and make large wind turbines stable under high winds.)
e.g. I can tell you things act like a spring near (stable) equilibrium, and you can believe me, but why on Earth would that be true? Well, Taylor expand the potential at equilibrium. Define V(0)=0, and equilibrium means V'(0)=0, so V(x) ~ V''(0)/2 x^2, so F = -dV/dx = -V''(0)x, which is a spring with spring constant k=V''(0).
That's all a very conceptual explanation; the point is near an equilibrium, zoom in and you have a parabolic potential! What is the potential for a spring? A parabola! This is basic Calc BC stuff, but it also justifies why we might care about about simple harmonic motion. Calculus is the whole business of "zooming in."
A lot of it I think is just training people to adopt a "physics-like" or "math-like" way of thinking and giving them a general overview of how things work.
A factory needs to produce 12,000 components per year. Each production run costs $300 to set up, and storing one component costs $4 per year. What production quantity Q minimizes the annual setup and storage costs?
Doing one run each month (quantity = 1,000 a month) would entail setup costs of 3,600. And storage costs of 4 * average storage of 500 components = 2,000. For a total cost of 5,600.
All according to the given model, of course, but I think this is the general idea.
How long does a production run take and how many units can you do in a single sun? Since this isn't mentioned, the answer is to produce everything at the last second of the year. But we are also missing information on why the factory needs to produce 12,000 components in a year and for whom and about the logistics involved in getting those components to the buyer.
I always hated these type of questions for their lack of precision. You haven't even mentioned how many units in a single production run will be faulty and need to be scrapped instead of delivered, how am I supposed to optimize anything?!