Graphs 6
2 marks · HardA company models the cost, $C, in dollars, of producing x batches of items by the equation below. \[ C = \frac{1800}{x} + 70x \] For what value of x is the cost C minimized (to the nearest whole number)?
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5 (±1)
Also accept: 5; 5 (nearest integer)
Common mistakes: Using x = 0 (undefined); Selecting x = 1 or x = 6; Mistaking for maximum
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Marking points
M1 · 1 mark · Substitutes several integer values (x = 2, 3, 4, 5, 6, etc.) or sets up an approach to find the minimum value.
A1 · 1 mark · Finds x = 5 (or nearest integer in the range) for minimum cost.
Worked solution
Let us try integer values of x since x > 0.
| x | C |
|---|---|
| 2 | 900 + 140 = 1040 |
| 3 | 600 + 210 = 810 |
| 4 | 450 + 280 = 730 |
| 5 | 360 + 350 = 710 |
| 6 | 300 + 420 = 720 |
The minimum cost occurs at x = 5 (nearest integer).