Question 2 To earn extra money in the summer you grow tomato

Question 2. To earn extra money in the summer, you grow tomatoes and sell them at the farmers\' market for $.60 pound. By adding compost to your garden, you can increase your yield as shown in the table below. If compost cost $6.50 per 10 pound bag and your goal is to make as much money as possible, how many 10 pound bag of compost should you add? Show your work. Think marginally! (marginal benefit versus marginal cost) Pounds of Tomatoes 300 318 334 347 358 364 367 Pounds of Compost 10 20 30 40

Solution

The benefit of adding a pound of compost is the extra revenue you’ll get from the extra tomatoes that result. The cost of adding a pound of compost is $6.5. By adding the 40 pound of compost you’ll get 11 extra pounds of tomatoes, or $6.6 in extra revenue, which more than covers the $6.5 cost of the extra pound of compost. But adding the 50 pound of compost gives only 6 extra pounds of tomatoes, so the corresponding revenue increase ($3.6) is less than the cost of the compost. You should add 40 pounds of compost and no more

Pounds of compost	Pounds of Tomatos	Marginal Cost	Marginal Benefit	Marginal Benefit ($)	Net Benefit	Marginal net benefit
0	300	6.5	0	0	0
10	318	6.5	18	10.8	4.3	4.3
20	334	6.5	16	9.6	7.4	3.1
30	347	6.5	13	7.8	8.7	1.3
40	358	6.5	11	6.6	2.3	-6.4
50	364	6.5	6	3.6	-0.6	-2.9
60	367	6.5	3	1.8	-5.3	-4.7