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Answer:
- Purchase fewer than 15 jerseys from Print It; purchase more than 15 jerseys from Top Print; purchase exactly 15 jerseys from any supplier
- Value Printing could charge a $15 one-time charge and $20 per jersey
Step-by-step explanation:
1. For x jerseys, the cost from Print It is $21 each, so ...
p = 21x
The cost from Top Print is less per shirt, but has a set-up charge. Its cost can be modeled by ...
t = 45 +18x
These two costs will be the same when ...
p = t
21x = 45 +18x
3x = 45
x = 15
Purchasing 15 shirts from either supplier will cost $21·15 = $315. The lower per-jersey cost at Top Print will come into play if more than 15 shirts are ordered.
- Bill should order fewer than 15 shirts from Print It, and more than 15 shirts from Top Print.
- An order of exactly 15 shirts will cost the same from any supplier.
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2. Value Printing wants their pricing to be somewhere between the prices of the other two shops. That means their per-jersey cost will be somewhere between $18 and $21, and their setup cost will be less than $45. It also means their cost for 15 jerseys must be exactly $315, as it is for both other shops.
If we choose a per-jersey cost of $20 for Value Printing, then the setup cost must be ($315 -$20×15) = $15 in order for the cost of 15 jerseys to match the cost at the other shops. With these choices, at Value Printing, ...
- pay a one-off setup cost of $15
- then each jersey will cost $20
