Assume that the mathematical model C(x) = 16x + 130 represents the cost C, in hundreds of dollars, for a certain manufacturer to produce x items. How many items x can be manufactured while keeping costs between $525,000 and $781,000? Thanks in advance!
C is in hundred so divide by 100
substitute in C = 5250 and solve for x
substitute in C = 7810 and solve for x
C(x) =16x+130 {x| 320 < x <480
525,000/100
5,250=16x+130
16x=5,250-130
16x=5,120
x=5,120/16
x=320
781,000/100
7,810=16x+130
16x=7,810-130
16x=7,680
x=7,680/16
x=480
Then if that is true then this is the solution? I think I got it!
so anything between those numbers 320 and 480 if you did the arithmetic right
To find the number of items that can be manufactured while keeping costs between $525,000 and $781,000, we need to solve the inequality with respect to x, given by:
525,000 ≤ 16x + 130 ≤ 781,000
We'll solve this inequality step by step.
Step 1: Subtract 130 from all parts of the inequality:
525,000 - 130 ≤ 16x + 130 - 130 ≤ 781,000 - 130
524,870 ≤ 16x ≤ 780,870
Step 2: Divide all parts of the inequality by 16:
524,870/16 ≤ 16x/16 ≤ 780,870/16
32,805.625 ≤ x ≤ 48,804.375
Since x represents the number of items, it should be a whole number. However, the inequality gives us a range of values for x rather than a specific value. Therefore, the number of items that can be manufactured while keeping costs between $525,000 and $781,000 should be a whole number between 32,806 and 48,804 (inclusive).
Note: Keep in mind that since the cost is measured in hundreds of dollars, the result is given in terms of hundreds of items.