143-01 Summer 2018-Section 1 Malia Remillard | 7/12/18 8:36 PM Homework: Section

Question

143-01 Summer 2018-Section 1 Malia Remillard | 7/12/18 8:36 PM Homework: Section 4.2 Score: 0 of 1 pt 4.2.14 11 of 15 (1 complete) HW Score: 6.67%, 1 of 15 pts Question Help An orange grove produces a profit of $100 per tree when there are 1100 trees planted Because of overcrowding, the profit per tree (for every tree in the grove) is reduced by 4 cents per tree for each one additional tree planted How many trees should be planted in order to maximize the total profit of the orange grove? What is the maximum profit? How many trees should be planted in order to maximize the total profit of the orange grove?

Explanation / Answer

Let x be number of tress planted

P=(100-0.04x)(1100+x)=100*1100-0.04*1100x-0.04x^2+100x=-0.04x2+56x+110000

dp/dx=-0.08x+56

for max dp/dx=0

0.08x=56

x=700(100

maximum profit occurs for 700 tress maximum profit =(100-0.04x)(1100+x)=(100-0.04*700)(1100+700)=$129600

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