Question

My Notes Your small farm encompasses 110 acres, and you are planning to grow tomatoes, lettuce, and carrots in the coming planting season. Fertilizer costs per acre are: $5 for tomatoes, $4 for lettuce, and $2 for carrots. Based on past experience, you estimate that each acre of tomatoes will require an average of 4 hours of labor per week, while tending to lettuce and carrots will each require an average of 2 hours per week. You estimate a profit of $3,000 for each acre of tomatoes, $1,400 for each acre of lettuce and $400 for each acre of carrots. You would like to spend at least $440 on fertilizer (your niece owns the company that manufactures it) and your farm laborers can supply up to 550 hours per week. How many acres of each crop should you plant to maximize total profits?

Answer 1

Answer:

For maximum profit, we'll take tomato.

Explanation:

Total = 110 Acres

                               Toamto         Lettuce        carrots

Fertilize                   5                    4                  2

Labour                    4Hr/W            2Hr/W         2Hr/W

Fertilize                  5x+4x+2X=440 it means, x=40.

                              5(40); 4(40) : 2(40)

Labour                    4x+2x+2x= 550 it means, x=68.75

                               4(68.75); 2(68.75); 2(68.75);

Profit                       3000                1400           400

Expenses               475                   297.5          217.5

Differemce of profit  2525            1102.5          232.5

Hence tomatos are best profitable.