Question

Art Kumar lives on the outskirts of Draper and has a 1-acre lot next to his home. He plans to grow vegetables on the lot and sell them at the downtown market during the summer. He doesn’t have enough time to grow the vegetables himself, so he has hired a local college student to plant and tend the garden and sell the crops at the market. Art is considering five vegetables to plant that seem to be popular at the market—asparagus, corn, tomatoes, green beans, and red peppers. Art estimates the following yields per acre for each vegetable—2,000 pounds of asparagus, 7,200 pounds of corn, 25,000 pounds of tomatoes, 3,900 pounds of green beans, and 12,500 pounds of red peppers. The costs per acre are $1,800 for asparagus, $1,740 for corn, $6,000 for tomatoes, $3,000 for green beans, and $2,700 for red peppers. Asparagus sells for $1.90 per pound, corn sells for $0.10 per pound, tomatoes sell for $3.25 per pound, green beans sell for $3.40 per pound, and red peppers sell for $3.45 per pound. He has budgeted $5,000 for the garden. Talking to some of the other market vendors, he estimates that he will not sell more than 1,200 pounds of asparagus, 10,000 pounds of tomatoes, 2,000 pounds of green beans, and 5,000 pounds of red peppers. Art wants to know the portion of his lot that he should plant with each vegetable to maximize his revenue.

Answer 1

10,000 pounds of Tomatoes; 780 pounds of Green Beans; and 5,000 pounds of Red Pepper.

Step-by-step explanation:

The following information was provided in the question and computed.

Yield per acre (pound): 2,000 (asparagus), 7,200 (corn), 25,000 (tomatoes), 3,900 (green beans), 12,500 (red pepper).

Cost per acre: $1,800 (asparagus), $1,740 (corn), $6,000 (tomatoes), $3,000 (green beans), $2,700 (red pepper).

Selling price per pound: $1.90 (asparagus), $0.10 (corn), $3.25 (tomatoes), $3.40 (green beans), $3.45 (red pepper).

Sales volume limit (pound): 1,200 (asparagus), nil (corn), 10,000 (tomatoes), 2,000 (green beans), 5,000 (red pepper).

Given the above, we compute the cost per pound for each vegetable as follows:
`(Cost Per Acre)/(Yield Per Acre)`

Cost per pound: $0.9 (asparagus), $0.24 (corn), $0.24 (tomatoes), $0.77 (green beans), $0.22 (red pepper).

Using selling price per pound and Cost per pound, we compute the contribution per pound for each vegetable as follows:
`Selling Price Per Pound - Cost Per Pound`

Contribution per Pound: $1.00 (asparagus), -$0.14 (corn), $3.01 (tomatoes), $2.63 (green beans), $3.23 (red pepper).

To maximize revenue and profit, Art must focus on the vegetables with the highest contribution per Pound, in the following order.

4th (asparagus), 5th (corn), 2nd (tomatoes), 3rd (green beans), 1st (red pepper).

He will therefore plant according to the limit (volume) he can sell in the market.

1st plant: Red pepper = 5,000 pounds market limit (using
`(Sales Limit)/(Yield per Acre) = (5,000)/(12,000)` = 40% of the land available).

2nd plant: Tomatoes = 10,000 pounds market limit (using
`(10,000)/(25,000)` = 40% of the land available).

3rd plant: Green beans = using 20% of the land left = 20% * 3,900 yield per acre = 780 pounds.