Answer
corn 250 acres, wheat 500 acres, and soybeans 450 acres,
Work Step by Step
Step 1. Identify the quantities given in the Exercise: total acres $A=1200$ dollars, cost to grow corn per acre $r_1=45$, cost to grow wheat per acre $r_2=60$, and cost to grow soybeans per acre $r_3=50$, acres to grow wheat is twice of that of corn $A_2=2A_1$, total targeted costs $C=63750$ dollars.
Step 2: Establish equations based on the information given: cost to grow corn $C_1=r_1A_1=45A_1$, cost to grow wheat $C_2=r_2A_2=60\times2A_1=120A_1$, and cost to grow soybean $C_3=r_3A_3=50(1200-A_1-A_2)=50(1200-3A_1)$,
Step 3. The total cost equals to the sum of the above individual cost, so we have $C_1+C_2+C_3=C$ and $45A_1+120A_1+50(1200-3A_1)=63750$
Step 4. Solve the above equation by combining like terms to get $15A_1=3750$, $A_1=250$ acres, and $A_2=2A_1=500$ acres, and $A_3=1200-3A_1=450$ acres.
Step 5. We conclude that the acres for corn is 250, the acres for wheat is 500, and the acres for soybeans is 450.
