A company is considering two insurance plans with coverage and premiums shown in the table.$($For example, this means that$$ $$50$ buys one unit of plan$$ A$,$ consisting of$$ $$10,000$ fire and theft insurance and$$ $$180,000$ of liability$$ insurance.$)$ Answer parts a and b$.$

Policy A

Policy B

$$Fire$/$Theft

$$$$10,000$

$$$$15,000$

Liability

$$$$180,000$

$$$$120,000$

Premium

$$$$50$

$$$$40$

Question content area bottom

Part $1$

a$.$ The company needs at least $$$$300$ comma $000$ fire and theft insurance and at least $ $4$ comma $800$ comma $000$ liability from these plans. How many units should be purchased from each plan to minimize

the cost of the$$ premiums? What is the minimum$$ premium?

The company should purchase

$$

enter your response here units of Policy A and

$$

enter your response here units of Policy$$ B$,$ for a premium of $$$

$$

enter your response here.