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The total cost (in dollars) of ordering x custom shirts is represented by the piecewise function.

a) C(x)=15x for 0≤x<10, C(x)=12x for 0x≥10
b) C(x)=12x for 0≤x<10, C(x)=15x for 0x≥10
c) C(x)=15x for x≥10, C(x)=12x for 0≤x<10
d) C(x)=12x for x≥10, C(x)=15x for 0≤x<10

1 Answer

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Final answer:

The correct piecewise function likely represents a bulk discount pricing strategy, with a cost of $15 per shirt for fewer than 10 shirts and $12 per shirt for 10 or more shirts. The options given could be misprints, but options a and c are correct based on common pricing strategies.

Step-by-step explanation:

The student's question is about determining the correct piecewise function that describes the total cost, in dollars, of ordering a certain number of custom shirts. A piecewise function is a function that is defined by different expressions based on different intervals of the domain. Let's analyse the given options to find the right piecewise function:

  • Option a: C(x) = 15x for 0≤x<10, C(x) = 12x for x≥10. This suggests a price of $15 per shirt for fewer than 10 shirts, and a discounted price of $12 per shirt for 10 or more shirts.
  • Option b: C(x) = 12x for 0≤x<10, C(x) = 15x for x≥10. This suggests a lower price for fewer than 10 shirts, and a higher price for 10 or more shirts, which doesn't follow a typical bulk discount practice.
  • Option c: C(x) = 15x for x≥10, C(x) = 12x for 0≤x<10. This is just another way to phrase option a, with the intervals reversed.
  • Option d: C(x) = 12x for x≥10, C(x) = 15x for 0≤x<10. This is similar to option b and doesn't make sense in terms of pricing strategy.

Based on common bulk pricing strategies, the correct function would be either option a or option c, as they both represent a situation where there's a discount for purchasing a larger quantity (10 or more shirts in this case). Without additional context on whether the student meant to differentiate between options a and c or if it was a typographical mistake, we cannot definitively choose between them. However, the logic of bulk discount pricing would mean that the cost is $15 per shirt for fewer than 10 shirts and $12 per shirt for 10 or more shirts.

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