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The coffee variety Arabica yields about 750 kg of coffee beans per hectare, while
Robusta yields about 1200 kg per hectare. Suppose that a plantation has a
hectares of Arabica and r hectares of Robusta.

a. Write an equation relating a and r if the plantation yields 1,000,000 kg of coffee.

b. On August 14, 2003, the world market price of coffee was $1.42 per kg of Arabica
and $0.73 per kg of Robusta. Write an equation relating a and r if the plantation
produces coffee worth $1,000,000.

Sagot :

mhanifa

Answer:

  • See below

Step-by-step explanation:

a)

  • Arabica coffee = 750a
  • Robusta coffee = 1200r

The total amount coffee beans

  • 750a + 1200r = 1000000 kg

b)

The total amount of market price

  • 1.42*750a + 0.73*1200r = 1000000 ⇒
  • 1065a + 876r = 1000000 dollars
semsee45

Answer:

a)   750a + 1200r = 1000000

b)   1065a + 876r = 1000000

Step-by-step explanation:

Define the variables:

  • Let a = number of hectares of Arabica beans
  • Let r = number of hectares of Robusta beans

Part (a)

Given:

  • Arabica coffee = 750 kg beans per hectare
  • Robusta coffee = 1200 kg beans per hectare

If the plantation yields 1,000,000 kg of coffee:

⇒ 750a + 1200r = 1000000

Part (b)

Given:

  • Arabica beans = $1.42 per kg
  • Robusta beans = $0.73 per kg

If the price of Arabica beans is $1.42 per kg, and Arabica yields about 750 kg per hectare, then the price per hectare of Arabica coffee beans is:

⇒ $1.42 × 750 = $1065 per hectare

If the price of Robusta beans is $0.73 per kg, and Robusta yields about 1200 kg per hectare, then the price per hectare of Robusta coffee beans is:

⇒ $0.73 × 1200 = $876 per hectare

Therefore, if the plantation produces coffee worth $1,000,000:

⇒ 1065a + 876r = 1000000

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