1. **State the problem:** We have a supply function $$S(p) = 0.08p^3 + 2p^2 + 10p + 11$$ and need to find the change in the number of units supplied when the price changes from $$p=18.00$$ to $$p=18.20$$. 2. **Formula and approach:** To find the change in supply, calculate $$S(18.20) - S(18.00)$$. 3. **Calculate $$S(18.00)$$:** $$S(18) = 0.08(18)^3 + 2(18)^2 + 10(18) + 11$$ Calculate powers: $$18^3 = 5832, \quad 18^2 = 324$$ Substitute: $$S(18) = 0.08 \times 5832 + 2 \times 324 + 180 + 11$$ $$= 466.56 + 648 + 180 + 11 = 1305.56$$ 4. **Calculate $$S(18.20)$$:** $$S(18.2) = 0.08(18.2)^3 + 2(18.2)^2 + 10(18.2) + 11$$ Calculate powers: $$18.2^3 = 6028.568, \quad 18.2^2 = 331.24$$ Substitute: $$S(18.2) = 0.08 \times 6028.568 + 2 \times 331.24 + 182 + 11$$ $$= 482.28544 + 662.48 + 182 + 11 = 1337.76544$$ 5. **Find the change in supply:** $$\Delta S = S(18.2) - S(18) = 1337.76544 - 1305.56 = 32.20544$$ 6. **Conclusion:** The manufacturer should supply approximately $$32.20$$ units more when the price increases from 18.00 to 18.20. **Final answer:** B. 32.20