## Related questions with answers

A farmer has three hundred acres of arable land on which she wants to plant cauliflower and cabbage. The farmer has $\$ 17,500$ available for planting and $\$ 12,000$ for fertilizer. Planting 1 acre of cauliflower costs $\$ 70$, and planting 1 acre of cabbage costs $\$ 35$. Fertilizer costs $\$ 25$ for 1 acre of cauliflower and $\$ 55$ for 1 acre of cabbage.

(a) Find a system of inequalities that describes the number of acres of each crop that the farmer can plant with the available resources. Graph the feasible region.

(b) Can the farmer plant one hundred fifty-five acres of cauliflower and one hundred fifteen acres of cabbage?

(c) Can the farmer plant one hundred fifteen acres of cauliflower and one hundred seventy-five acres of cabbage?

Solution

Verified**(a)**

We have two types of vegetables. Let's denote with $x$ and $y$ each type of them. Hence,

- with $x$, the number of acres planted with the vegetable type of 1,
- with $y$, the number of acres planted with the vegetable type of 2.

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