A farmer in Wood County has 1, 050 acres of land. She is going to plant each acr

Question

A farmer in Wood County has 1, 050 acres of land. She is going to plant each acre with corn, soybeans, or wheat. Each acre planted with corn yields a $2, 350 profit; each with soybeans yields $2, 350 profit; and each with wheat yields $2, 550 profit. She has 212 workers and 260 tons of fertilizer. The table below shows the requirement per acre of each of the crops. Assuming a linear relationship, use Excel Solver to determine the optimal planting mix of corn, soybeans, and wheat to maximize her profits. In formulating your linear program, do NOT restrict the three decision variables to integer values. (However, round the final values of these decision variables to the nearest whole number when entering those answers. Use these rounded decision variable values to compute "Total Profit" and enter that answer to the nearest whole number. Lastly, also use the rounded decision variable values to compute the three "Resources Used" answers and enter them to the nearest whole number. Leave no cells blank - be certain to enter "0" wherever required.)

Explanation / Answer

Below is the LPP formulation

Maximize Profit = 2350x + 2350y + 2250z
subject to,
0.2x + 0.3y + 0.3z <= 212
0.3x + 0.1y + 0.2z <= 260
x + y + z <= 1050

Hence
Decision for corn 811
Decision for soybean 166
Decision for wheat 0
Total prfit = 2293600

Resouces used
Labor (workers) 212
Fertilizer (tons) 260

Solver Solution x y z Total Demand Decision Variables 811.4286 165.7143 0 Profit 2350 2350 2250 2296286 Constraint 1 0.2 0.3 0.3 212 212 Constraint 2 0.3 0.1 0.2 260 260 Constraint 3 1 1 1 977.1429 1050

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.