MediumOptimization

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.2 Maximum and Minimum Problems, #34 · Calculus · Optimization

The figure for this exercise is in the book and isn't reproduced…

, we make and sell x pizzas. The income is R(x) = ax + bx2 and the cost is C(x) = c + dx + ex2.

Figure B shows $R (x) = 3 x - x^{2}$ and $C_{1} (x) = 1 + x^{2}$ and $C_{2} (x) = 2 + x^{2}$ . With cost $C_{1}$ , which sales $x$ makes a profit? Which $x$ makes the most profit? With higher fixed cost in $C_{2}$ , the best plan is ____.

The cookie box and popcorn box were created by Kay Dundas from a $1 2^{''} \times 1 2^{''}$ square. A box with no top is a calculus classic.

The figure for this exercise is in the book and isn't reproduced here.

This problem refers to a figure in its source book that isn't reproduced here.

~8 minWritten answer · check your work with Lemma

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.2 Maximum and Minimum Problems, #34

Stuck? A gentle nudge

No hints for this one.

Something off?

Workspace

Your working

Check your full solution

Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.

Your first check today doesn't need an account.

Your photos and PDFs are read once and not stored — only the transcription is kept.