Chapter 2.3, Problem 83E

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10th Edition

Soo T. Tan

ISBN: 9781285464640

Textbook Problem

**Profit of a Vineyard** Phillip, the proprietor of a vineyard, estimates that if 10,000 bottles of wine were produced this season, then the profit would be $5/bottle. But if more than 10,000 bottles were produced, then the profit per bottle for the entire lot would drop by $0.0002 for each additional bottle sold.

Assume that at least 10,000 bottles of wine are produced and sold, and let *x* denote the number of bottles produced and sold in excess of 10,000.

**a.**Find a function*P*giving the profit in terms of*x*.**b.**What is the profit Phillip can expect from the sale of 16,000 bottles of wine from his vineyard?

(a)

To determine

The function *P* that gives the profit in the variable of *x*.

Explanation

**Given information:**

The profit would be $5/bottle if 10,000 bottles are produced. If more than 10,000 bottles are produced, then the profit per bottle would drop by $0.0002 for each additional bottle sold.

**Calculation:**

Let *x* be the number of bottles produced and sold in excess of 10,000, then the total number of bottles produced and sold becomes

The profit per bottle is $5, for each bottle sold in excess of 10,000, the profit decreases by $0.0002 per bottle, so the profit per bottle becomes

(b)

To determine

The profit for the sale of 16,000 bottles.

Sect-2.1 P-1CQSect-2.1 P-2CQSect-2.1 P-3CQSect-2.1 P-4CQSect-2.1 P-1ESect-2.1 P-2ESect-2.1 P-3ESect-2.1 P-4ESect-2.1 P-5ESect-2.1 P-6E

Sect-2.1 P-7ESect-2.1 P-8ESect-2.1 P-9ESect-2.1 P-10ESect-2.1 P-11ESect-2.1 P-12ESect-2.1 P-13ESect-2.1 P-14ESect-2.1 P-15ESect-2.1 P-16ESect-2.1 P-17ESect-2.1 P-18ESect-2.1 P-19ESect-2.1 P-20ESect-2.1 P-21ESect-2.1 P-22ESect-2.1 P-23ESect-2.1 P-24ESect-2.1 P-25ESect-2.1 P-26ESect-2.1 P-27ESect-2.1 P-28ESect-2.1 P-29ESect-2.1 P-30ESect-2.1 P-31ESect-2.1 P-32ESect-2.1 P-33ESect-2.1 P-34ESect-2.1 P-35ESect-2.1 P-36ESect-2.1 P-37ESect-2.1 P-38ESect-2.1 P-39ESect-2.1 P-40ESect-2.1 P-41ESect-2.1 P-42ESect-2.1 P-43ESect-2.1 P-44ESect-2.1 P-45ESect-2.1 P-46ESect-2.1 P-47ESect-2.1 P-48ESect-2.1 P-49ESect-2.1 P-50ESect-2.1 P-51ESect-2.1 P-52ESect-2.1 P-53ESect-2.1 P-54ESect-2.1 P-55ESect-2.1 P-56ESect-2.1 P-57ESect-2.1 P-58ESect-2.1 P-59ESect-2.1 P-60ESect-2.1 P-61ESect-2.1 P-62ESect-2.1 P-63ESect-2.1 P-64ESect-2.1 P-65ESect-2.1 P-66ESect-2.1 P-67ESect-2.1 P-68ESect-2.1 P-69ESect-2.1 P-71ESect-2.1 P-72ESect-2.1 P-73ESect-2.1 P-74ESect-2.1 P-75ESect-2.1 P-76ESect-2.1 P-77ESect-2.1 P-78ESect-2.1 P-79ESect-2.1 P-80ESect-2.1 P-81ESect-2.1 P-82ESect-2.1 P-83ESect-2.1 P-84ESect-2.1 P-85ESect-2.1 P-86ESect-2.1 P-87ESect-2.1 P-88ESect-2.1 P-89ESect-2.1 P-90ESect-2.1 P-91ESect-2.1 P-92ESect-2.1 P-93ESect-2.1 P-94ESect-2.1 P-95ESect-2.1 P-96ESect-2.1 P-97ESect-2.1 P-98ESect-2.1 P-1TESect-2.1 P-2TESect-2.1 P-3TESect-2.1 P-4TESect-2.1 P-5TESect-2.1 P-6TESect-2.1 P-7TESect-2.1 P-8TESect-2.1 P-9TESect-2.1 P-10TESect-2.1 P-11TESect-2.1 P-12TESect-2.1 P-13TESect-2.1 P-14TESect-2.1 P-15TESect-2.2 P-1CQSect-2.2 P-2CQSect-2.2 P-3CQSect-2.2 P-4CQSect-2.2 P-5CQSect-2.2 P-6CQSect-2.2 P-1ESect-2.2 P-2ESect-2.2 P-3ESect-2.2 P-4ESect-2.2 P-5ESect-2.2 P-6ESect-2.2 P-7ESect-2.2 P-8ESect-2.2 P-9ESect-2.2 P-10ESect-2.2 P-11ESect-2.2 P-12ESect-2.2 P-13ESect-2.2 P-14ESect-2.2 P-15ESect-2.2 P-16ESect-2.2 P-17ESect-2.2 P-18ESect-2.2 P-19ESect-2.2 P-20ESect-2.2 P-21ESect-2.2 P-22ESect-2.2 P-23ESect-2.2 P-24ESect-2.2 P-25ESect-2.2 P-26ESect-2.2 P-27ESect-2.2 P-28ESect-2.2 P-29ESect-2.2 P-30ESect-2.2 P-31ESect-2.2 P-32ESect-2.2 P-33ESect-2.2 P-34ESect-2.2 P-35ESect-2.2 P-36ESect-2.2 P-37ESect-2.2 P-38ESect-2.2 P-39ESect-2.2 P-40ESect-2.2 P-41ESect-2.2 P-42ESect-2.2 P-43ESect-2.2 P-44ESect-2.2 P-45ESect-2.2 P-46ESect-2.2 P-47ESect-2.2 P-48ESect-2.2 P-49ESect-2.2 P-50ESect-2.2 P-51ESect-2.2 P-52ESect-2.2 P-53ESect-2.2 P-54ESect-2.2 P-55ESect-2.2 P-56ESect-2.2 P-57ESect-2.2 P-58ESect-2.2 P-59ESect-2.2 P-60ESect-2.2 P-61ESect-2.2 P-62ESect-2.2 P-63ESect-2.2 P-64ESect-2.2 P-65ESect-2.2 P-66ESect-2.2 P-67ESect-2.2 P-68ESect-2.2 P-69ESect-2.2 P-70ESect-2.2 P-71ESect-2.2 P-72ESect-2.2 P-73ESect-2.2 P-74ESect-2.2 P-75ESect-2.2 P-76ESect-2.2 P-77ESect-2.2 P-78ESect-2.3 P-1CQSect-2.3 P-2CQSect-2.3 P-3CQSect-2.3 P-1ESect-2.3 P-2ESect-2.3 P-3ESect-2.3 P-4ESect-2.3 P-5ESect-2.3 P-6ESect-2.3 P-7ESect-2.3 P-8ESect-2.3 P-9ESect-2.3 P-10ESect-2.3 P-11ESect-2.3 P-12ESect-2.3 P-13ESect-2.3 P-14ESect-2.3 P-15ESect-2.3 P-16ESect-2.3 P-17ESect-2.3 P-18ESect-2.3 P-19ESect-2.3 P-20ESect-2.3 P-21ESect-2.3 P-22ESect-2.3 P-23ESect-2.3 P-24ESect-2.3 P-25ESect-2.3 P-26ESect-2.3 P-27ESect-2.3 P-28ESect-2.3 P-29ESect-2.3 P-30ESect-2.3 P-31ESect-2.3 P-32ESect-2.3 P-33ESect-2.3 P-34ESect-2.3 P-35ESect-2.3 P-36ESect-2.3 P-37ESect-2.3 P-38ESect-2.3 P-39ESect-2.3 P-40ESect-2.3 P-41ESect-2.3 P-42ESect-2.3 P-43ESect-2.3 P-44ESect-2.3 P-45ESect-2.3 P-46ESect-2.3 P-47ESect-2.3 P-48ESect-2.3 P-49ESect-2.3 P-50ESect-2.3 P-51ESect-2.3 P-52ESect-2.3 P-53ESect-2.3 P-54ESect-2.3 P-55ESect-2.3 P-56ESect-2.3 P-57ESect-2.3 P-58ESect-2.3 P-59ESect-2.3 P-60ESect-2.3 P-61ESect-2.3 P-62ESect-2.3 P-63ESect-2.3 P-64ESect-2.3 P-65ESect-2.3 P-66ESect-2.3 P-67ESect-2.3 P-68ESect-2.3 P-69ESect-2.3 P-70ESect-2.3 P-71ESect-2.3 P-72ESect-2.3 P-73ESect-2.3 P-74ESect-2.3 P-75ESect-2.3 P-76ESect-2.3 P-77ESect-2.3 P-78ESect-2.3 P-79ESect-2.3 P-80ESect-2.3 P-81ESect-2.3 P-82ESect-2.3 P-83ESect-2.3 P-84ESect-2.3 P-85ESect-2.3 P-86ESect-2.3 P-87ESect-2.3 P-88ESect-2.3 P-1TESect-2.3 P-2TESect-2.3 P-3TESect-2.3 P-4TESect-2.3 P-5TESect-2.3 P-6TESect-2.3 P-7TESect-2.3 P-8TESect-2.3 P-9TESect-2.3 P-10TESect-2.3 P-11TESect-2.3 P-12TESect-2.3 P-13TESect-2.3 P-14TESect-2.3 P-15TESect-2.3 P-16TESect-2.3 P-17TESect-2.3 P-18TESect-2.3 P-19TESect-2.3 P-20TESect-2.4 P-1CQSect-2.4 P-2CQSect-2.4 P-3CQSect-2.4 P-4CQSect-2.4 P-5CQSect-2.4 P-1ESect-2.4 P-2ESect-2.4 P-3ESect-2.4 P-4ESect-2.4 P-5ESect-2.4 P-6ESect-2.4 P-7ESect-2.4 P-8ESect-2.4 P-9ESect-2.4 P-10ESect-2.4 P-11ESect-2.4 P-12ESect-2.4 P-13ESect-2.4 P-14ESect-2.4 P-15ESect-2.4 P-16ESect-2.4 P-17ESect-2.4 P-18ESect-2.4 P-19ESect-2.4 P-20ESect-2.4 P-21ESect-2.4 P-22ESect-2.4 P-23ESect-2.4 P-24ESect-2.4 P-25ESect-2.4 P-26ESect-2.4 P-27ESect-2.4 P-28ESect-2.4 P-29ESect-2.4 P-30ESect-2.4 P-31ESect-2.4 P-32ESect-2.4 P-33ESect-2.4 P-34ESect-2.4 P-35ESect-2.4 P-36ESect-2.4 P-37ESect-2.4 P-38ESect-2.4 P-39ESect-2.4 P-40ESect-2.4 P-41ESect-2.4 P-42ESect-2.4 P-43ESect-2.4 P-44ESect-2.4 P-45ESect-2.4 P-46ESect-2.4 P-47ESect-2.4 P-48ESect-2.4 P-49ESect-2.4 P-50ESect-2.4 P-51ESect-2.4 P-52ESect-2.4 P-53ESect-2.4 P-54ESect-2.4 P-55ESect-2.4 P-56ESect-2.4 P-57ESect-2.4 P-58ESect-2.4 P-59ESect-2.4 P-60ESect-2.4 P-61ESect-2.4 P-62ESect-2.4 P-63ESect-2.4 P-64ESect-2.4 P-65ESect-2.4 P-66ESect-2.4 P-67ESect-2.4 P-68ESect-2.4 P-69ESect-2.4 P-70ESect-2.4 P-71ESect-2.4 P-72ESect-2.4 P-73ESect-2.4 P-74ESect-2.4 P-75ESect-2.4 P-76ESect-2.4 P-77ESect-2.4 P-78ESect-2.4 P-79ESect-2.4 P-80ESect-2.4 P-81ESect-2.4 P-82ESect-2.4 P-83ESect-2.4 P-84ESect-2.4 P-85ESect-2.4 P-86ESect-2.4 P-87ESect-2.4 P-88ESect-2.4 P-89ESect-2.4 P-90ESect-2.4 P-91ESect-2.4 P-92ESect-2.4 P-93ESect-2.4 P-94ESect-2.4 P-95ESect-2.4 P-96ESect-2.4 P-97ESect-2.4 P-98ESect-2.4 P-1TESect-2.4 P-2TESect-2.4 P-3TESect-2.4 P-4TESect-2.4 P-5TESect-2.4 P-6TESect-2.4 P-7TESect-2.4 P-8TESect-2.4 P-9TESect-2.4 P-10TESect-2.4 P-11TESect-2.4 P-12TESect-2.5 P-1CQSect-2.5 P-2CQSect-2.5 P-3CQSect-2.5 P-4CQSect-2.5 P-5CQSect-2.5 P-6CQSect-2.5 P-1ESect-2.5 P-2ESect-2.5 P-3ESect-2.5 P-4ESect-2.5 P-5ESect-2.5 P-6ESect-2.5 P-7ESect-2.5 P-8ESect-2.5 P-9ESect-2.5 P-10ESect-2.5 P-11ESect-2.5 P-12ESect-2.5 P-13ESect-2.5 P-14ESect-2.5 P-15ESect-2.5 P-16ESect-2.5 P-17ESect-2.5 P-18ESect-2.5 P-19ESect-2.5 P-20ESect-2.5 P-21ESect-2.5 P-22ESect-2.5 P-23ESect-2.5 P-24ESect-2.5 P-25ESect-2.5 P-26ESect-2.5 P-27ESect-2.5 P-28ESect-2.5 P-29ESect-2.5 P-30ESect-2.5 P-31ESect-2.5 P-32ESect-2.5 P-33ESect-2.5 P-34ESect-2.5 P-35ESect-2.5 P-36ESect-2.5 P-37ESect-2.5 P-38ESect-2.5 P-39ESect-2.5 P-40ESect-2.5 P-41ESect-2.5 P-42ESect-2.5 P-43ESect-2.5 P-44ESect-2.5 P-45ESect-2.5 P-46ESect-2.5 P-47ESect-2.5 P-48ESect-2.5 P-49ESect-2.5 P-50ESect-2.5 P-51ESect-2.5 P-52ESect-2.5 P-53ESect-2.5 P-54ESect-2.5 P-55ESect-2.5 P-56ESect-2.5 P-57ESect-2.5 P-58ESect-2.5 P-59ESect-2.5 P-60ESect-2.5 P-61ESect-2.5 P-62ESect-2.5 P-63ESect-2.5 P-64ESect-2.5 P-65ESect-2.5 P-66ESect-2.5 P-67ESect-2.5 P-68ESect-2.5 P-69ESect-2.5 P-70ESect-2.5 P-71ESect-2.5 P-72ESect-2.5 P-73ESect-2.5 P-74ESect-2.5 P-75ESect-2.5 P-76ESect-2.5 P-77ESect-2.5 P-78ESect-2.5 P-79ESect-2.5 P-80ESect-2.5 P-81ESect-2.5 P-82ESect-2.5 P-83ESect-2.5 P-84ESect-2.5 P-85ESect-2.5 P-86ESect-2.5 P-87ESect-2.5 P-88ESect-2.5 P-89ESect-2.5 P-90ESect-2.5 P-91ESect-2.5 P-92ESect-2.5 P-93ESect-2.5 P-94ESect-2.5 P-95ESect-2.5 P-96ESect-2.5 P-97ESect-2.5 P-98ESect-2.5 P-99ESect-2.5 P-100ESect-2.5 P-101ESect-2.5 P-102ESect-2.5 P-1TESect-2.5 P-2TESect-2.5 P-3TESect-2.5 P-4TESect-2.5 P-5TESect-2.5 P-6TESect-2.5 P-7TESect-2.5 P-8TESect-2.5 P-9TESect-2.5 P-10TESect-2.5 P-11TESect-2.5 P-12TESect-2.6 P-1CQSect-2.6 P-2CQSect-2.6 P-3CQSect-2.6 P-4CQSect-2.6 P-5CQSect-2.6 P-6CQSect-2.6 P-1ESect-2.6 P-2ESect-2.6 P-3ESect-2.6 P-4ESect-2.6 P-5ESect-2.6 P-6ESect-2.6 P-7ESect-2.6 P-8ESect-2.6 P-9ESect-2.6 P-10ESect-2.6 P-11ESect-2.6 P-12ESect-2.6 P-13ESect-2.6 P-14ESect-2.6 P-15ESect-2.6 P-16ESect-2.6 P-17ESect-2.6 P-18ESect-2.6 P-19ESect-2.6 P-20ESect-2.6 P-21ESect-2.6 P-22ESect-2.6 P-23ESect-2.6 P-26ESect-2.6 P-27ESect-2.6 P-28ESect-2.6 P-29ESect-2.6 P-30ESect-2.6 P-31ESect-2.6 P-32ESect-2.6 P-33ESect-2.6 P-34ESect-2.6 P-35ESect-2.6 P-36ESect-2.6 P-37ESect-2.6 P-38ESect-2.6 P-39ESect-2.6 P-40ESect-2.6 P-41ESect-2.6 P-42ESect-2.6 P-43ESect-2.6 P-44ESect-2.6 P-45ESect-2.6 P-46ESect-2.6 P-47ESect-2.6 P-48ESect-2.6 P-49ESect-2.6 P-50ESect-2.6 P-51ESect-2.6 P-52ESect-2.6 P-53ESect-2.6 P-54ESect-2.6 P-55ESect-2.6 P-56ESect-2.6 P-57ESect-2.6 P-58ESect-2.6 P-59ESect-2.6 P-60ESect-2.6 P-61ESect-2.6 P-62ESect-2.6 P-1TESect-2.6 P-2TESect-2.6 P-3TESect-2.6 P-4TESect-2.6 P-5TESect-2.6 P-6TESect-2.6 P-7TESect-2.6 P-8TESect-2.6 P-9TESect-2.6 P-10TECh-2 P-1CRQCh-2 P-2CRQCh-2 P-3CRQCh-2 P-4CRQCh-2 P-5CRQCh-2 P-6CRQCh-2 P-7CRQCh-2 P-8CRQCh-2 P-9CRQCh-2 P-10CRQCh-2 P-11CRQCh-2 P-12CRQCh-2 P-13CRQCh-2 P-14CRQCh-2 P-1RECh-2 P-2RECh-2 P-3RECh-2 P-4RECh-2 P-5RECh-2 P-6RECh-2 P-7RECh-2 P-8RECh-2 P-9RECh-2 P-10RECh-2 P-11RECh-2 P-12RECh-2 P-13RECh-2 P-14RECh-2 P-15RECh-2 P-16RECh-2 P-17RECh-2 P-18RECh-2 P-19RECh-2 P-20RECh-2 P-21RECh-2 P-22RECh-2 P-23RECh-2 P-24RECh-2 P-25RECh-2 P-26RECh-2 P-27RECh-2 P-28RECh-2 P-29RECh-2 P-30RECh-2 P-31RECh-2 P-32RECh-2 P-33RECh-2 P-34RECh-2 P-35RECh-2 P-36RECh-2 P-37RECh-2 P-38RECh-2 P-39RECh-2 P-40RECh-2 P-41RECh-2 P-42RECh-2 P-43RECh-2 P-44RECh-2 P-45RECh-2 P-46RECh-2 P-47RECh-2 P-48RECh-2 P-49RECh-2 P-50RECh-2 P-51RECh-2 P-52RECh-2 P-53RECh-2 P-54RECh-2 P-55RECh-2 P-56RECh-2 P-57RECh-2 P-58RECh-2 P-59RECh-2 P-60RECh-2 P-61RECh-2 P-62RECh-2 P-63RECh-2 P-64RECh-2 P-1BMCh-2 P-2BMCh-2 P-3BMCh-2 P-4BMCh-2 P-5BMCh-2 P-6BM

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