3.
9 Optimization Homework Name _______________________________________________
1. A farmer has 350 feet of fencing to enclose 2 adjacent horse corrals. What dimensions should be
used so that the enclosed area will be a maximum?
2. A rectangle has its base on the x-axis and its two upper corners on the parabola 𝑦𝑦 = 12 − 𝑥𝑥 2 .
What is the largest possible area of the rectangle?
3. The owner of an orange grove estimates that if 24 trees are planted per acre, then each mature
tree will yield 600 oranges per year. For each additional tree planted per acre, the number of
oranges produces by each tree decrease by 12 per year. How many trees should be planted per
acre to obtain the most oranges per year?
© 2016 – 2018 Flamingo MathTM Jean Adams
4. A poster is being designed that is to contain 150 in.2 of printed material with margins of
2 inches at the top and bottom and 3 inches at each side. What overall dimensions will
minimize the amount of paper used?
5. Find the dimensions of the rectangle with a maximum area inscribed in a semi-circle with
radius 8 inches.
8000𝑡𝑡
6. The size of a bacteria population found in some food grows at a rate of 𝑃𝑃(𝑡𝑡) = 80 +𝑡𝑡 2 where 𝑡𝑡 is
measured in weeks. Determine when the bacteria will reach it’s maximize size. What is the
maximum size of the population?
© 2016 – 2018 Flamingo MathTM Jean Adams
7. An offshore well is 6 miles off the coast. A gas line is to be laid from the well to a refining
station that is 14 miles down the coast. The cost to lay the line is $23,000 per mile along the
shoreline and $32,000 per mile under the ocean. How should the gas line be laid at the least
expensive cost? What is the cost?
6 miles
x
14 miles
8. A boat leaves a dock at 2:00 pm and travels due south at a speed of 20 kilometers/hour.
Another boat has been heading due east at 15 kilometers/hour and reaches the same dock at
3:00 pm. At what time were the two boats closest together?
9. On a given day, the flow rate 𝐹𝐹 (cars per hour) on a congested roadway is given by
𝑣𝑣
𝐹𝐹(𝑣𝑣) = 16+0.02𝑣𝑣2 , where 𝑣𝑣 is the speed of the traffic in miles per hour. What speed will
maximize the flow rate on the road? Round your answer to the nearest mile per hour.
© 2016 – 2018 Flamingo MathTM Jean Adams
