The Toyota Co. has a daily production quota of $100,000 worth of cars. They produce two types of cars. Their compact model (x) is valued $10,000 and their luxury car (y) is valued at $20,000.
A. Write an inequality that describes the production quota
B. On April 6, the factory produced 5 compacts and 2 luxury cars. Was the company above, below or on target with their quota?
C. On August 31, the factory produced 9 compacts and 2 luxury cars. Was the company above, below or on target with their quota?
A. To write an inequality that describes the production quota, we need to determine the total value of cars produced each day, which should be greater than or equal to $100,000.
Let's express the number of compact cars as "x" and the number of luxury cars as "y". The value of a compact car is $10,000, so the value of x compact cars would be 10,000x. The value of a luxury car is $20,000, so the value of y luxury cars would be 20,000y.
Therefore, the inequality that describes the production quota is:
10,000x + 20,000y ≥ 100,000
B. On April 6, the factory produced 5 compact cars and 2 luxury cars. To determine if the company was above, below, or on target with their quota, we need to calculate the total value of cars produced on that day and compare it with the daily production quota.
Using the values given, the total value of the cars produced on April 6 would be:
(5 compact cars x $10,000) + (2 luxury cars x $20,000) = $50,000 + $40,000 = $90,000
Since $90,000 is less than the daily production quota of $100,000, the company was below target with their quota on April 6.
C. On August 31, the factory produced 9 compact cars and 2 luxury cars. To determine if the company was above, below, or on target with their quota, we again calculate the total value of cars produced and compare it with the daily production quota.
Using the values given, the total value of the cars produced on August 31 would be:
(9 compact cars x $10,000) + (2 luxury cars x $20,000) = $90,000 + $40,000 = $130,000
Since $130,000 is greater than the daily production quota of $100,000, the company was above target with their quota on August 31.