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Part $1$

Chris Sandvig$$ Irrigation, Inc., has summarized the price list from four potential suppliers of an underground control valve. See the table below. Annual usage is $800$valves; order cost is $$$$11$ per$$ order; and annual inventory holding costs are $$$$7\mathrm{.}55$ per unit.

$$

Vendor A

Vendor B

Vendor C

Vendor D

Quantity

Price

Quantity

Price

Quantity

Price

Quantity

Price

$1-9$

$$$$35\mathrm{.}00$

$1-14$

$$$$34\mathrm{.}75$

$1-24$

$$$$34\mathrm{.}50$

$1-74$

$$$$34\mathrm{.}25$

$10-14$

$34\mathrm{.}75$

$15-49$

$34\mathrm{.}00$

$25-74$

$33\mathrm{.}75$

$75-199$

$33\mathrm{.}00$

$15-49$

$33\mathrm{.}55$

$50-99$

$32\mathrm{.}80$

$75-199$

$32\mathrm{.}50$

$200+$

$31\mathrm{.}00$

$50-99$

$32\mathrm{.}35$

$100-299$

$31\mathrm{.}60$

$200+$

$31\mathrm{.}10$

$100-299$

$31\mathrm{.}15$

$300+$

$30\mathrm{.}50$

$300+$

$30\mathrm{.}75$

Part $2$

Which vendor should be selected and what order quantity is best if Sandvig Irrigation wants to minimize total$$ cost