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A souvenir shop sells about 200 coffee mugs each month for $6 each. The shop owner estimates that for each $0.50 increase in the price, he will sell about 10 fewer coffee mugs per month. How much should the owner charge for each mug in order to maximize the monthly income from their sales? What is the independent variable? The price (number of $0.50 increases) What is the dependent variable? Monthly income Example 1-4a
The income the number of mugs sold the price per mug. is times A souvenir shop sells about 200 coffee mugs each month for $6 each. The shop owner estimates that for each $0.50 increase in the price, he will sell about 10 fewer coffee mugs per month. x = the number of $0.50 price increases I(x)     = Example 1-4a
The mug price should be I(x) = so vertex is a maximum x This means that the shop should make 4 price increases of $0.50 to maximize their income.   Example 1-4a
What is the maximum monthly income the owner can expect to make from these items? = -80 + 160 + 1200 Answer:The maximum income is $1280. Example 1-4a

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Alg2 lesson 6-1 day 2

  • 1. A souvenir shop sells about 200 coffee mugs each month for $6 each. The shop owner estimates that for each $0.50 increase in the price, he will sell about 10 fewer coffee mugs per month. How much should the owner charge for each mug in order to maximize the monthly income from their sales? What is the independent variable? The price (number of $0.50 increases) What is the dependent variable? Monthly income Example 1-4a
  • 2. The income the number of mugs sold the price per mug. is times A souvenir shop sells about 200 coffee mugs each month for $6 each. The shop owner estimates that for each $0.50 increase in the price, he will sell about 10 fewer coffee mugs per month. x = the number of $0.50 price increases I(x) = Example 1-4a
  • 3. The mug price should be I(x) = so vertex is a maximum x This means that the shop should make 4 price increases of $0.50 to maximize their income. Example 1-4a
  • 4. What is the maximum monthly income the owner can expect to make from these items? = -80 + 160 + 1200 Answer:The maximum income is $1280. Example 1-4a