A farmer wants to plant peas and carrots on no more than 200 acres of his farm. If x represents the number of acres of peas and y represents the number of acres of carrots for solution (x, y), then which is a viable solution? A.(−50, 160) B.(80, 160) C.(75, −200) D.(60, 135)

Answer:Option D.(60, 135)Step-by-step explanation:Letx -----> the number of acres of peasy ----> the number of acres of carrotswe know thatThe inequality that represent the problem is equal to[tex]x+y\leq 200[/tex]soVerify each casecase A) (-50,160)substitute the value of x and the value of y in the inequality and then compare the result[tex]-50+160\leq 200[/tex][tex]110\leq 200[/tex] ----> is trueThe point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative numbercase B) (80,160)substitute the value of x and the value of y in the inequality and then compare the result[tex]80+160\leq 200[/tex][tex]240\leq 200[/tex] ----> is not truethereforeThe point is not a solution case C) (75,-200)substitute the value of x and the value of y in the inequality and then compare the result[tex]75-200\leq 200[/tex][tex]-125\leq 200[/tex] ----> is trueThe point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative numbercase D) (60,135)substitute the value of x and the value of y in the inequality and then compare the result[tex]60+135\leq 200[/tex][tex]195\leq 200[/tex] ----> is truethereforeThe point is a viable solution