Table $3\mathrm{.}4$: I am Ulysses

Uncle Ulysses operates a small business: he produces three types of houses to sell to people wanting to get back to nature. Based on your discussion with your uncle you construct the following table based on your understanding of his weekly availability of labor.

Item Profit$/$Unit Fabrication Assembly Painting Crating

Birdhouse $$1512\mathrm{.}510\mathrm{.}25$

Doghouse $$351\mathrm{.}251\mathrm{.}50\mathrm{.}50\mathrm{.}5$

Outhouse $$581\mathrm{.}75420\mathrm{.}75$

Capacity $30$ hours $50$ hours $20$ hours $20$ hours

Based on the information in the table, you formulate the problem as a linear program. The labor needed for fabrication, assembly, painting, and crating is all dedicated solely to each function, i$.$e$.,$ none of the workers have been cross$-$trained. The Excel solution and the answer and sensitivity report are shown below.

The Answer Report:

The Sensitivity Report:

Uncle Ulysses can obtain an additional $10$ hours of painting capacity free of charge by training his helper monkey to paint. If he did this, how would his profits be affected?

Group of answer choices

Profit would increase by $$6\mathrm{.}92.$

Profits would decrease by $$20.$

Profits would increase by $$1\mathrm{.}58.$

Cannot tell from the information provided.