Question

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, $1,500 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? HINT [See Example 3.] tomatoes acre(s) lettuce acre(s) carrots acre(s) profit In this event, will you be using all 110 acres of your farm? O Yes O No

Answer 1

Answer:
Given that Total = 10 acres . Fertilize - Tomatoes lettuce Carrots Labor uhelw a helw 2hrw. Fertilize = 5x + 4x + 20 = 440 11x = 440 x 440 x=40 -= luc)+ 4(40) : 2 (40) Labor = x + 2x + 2x = 550 ex = 550 2 - 550 x = 68.75 = 4(68.75):1068.75): 2168.75) Prokt = $ 3000, $1500, $400 Expendte for fertilizes labor hr Tomato S(40)+4(68.75) = 4175 Expendt for fertilize labor for lettuce . (40) + 2 (68.7) = 997.5 Expendite for fertilize labor for Carrots 2140) + 2(68.75 = 217.5

Differente do Pooht Eack Vesition - $(3000-475), (1500-297.5), (400 - 217.5) = 'lomaton = 2525 acry. - Lettuce = 1202.5 acres - Carrots = 182.5 acres Co . to maximum Profit & 2525 Proft we have acres. Tomato Yes In this event we will be using all no acres of the farm.