answer the following and explain

PROCEDURE Strategy for Solving Optimization Problems Step 1 Introduce variables, look for relationships among the variables, and con- struct a mathematical model of the form Maximize (or minimize) f(x)on the interval / Step 2 Find the critical values of fx). Step 3 Use the procedures developed in Section 5-5 to find the absolute maxi- mum (or minimum) value of (x) on the interval / and the value(s) of x where this occurs. Step 4 Use the solution to the mathematical model to answer all the questions asked in the problem. Example 1: Maximizing Area A homeowner has $320 to spend on building a fence around a rectangular garden. Three sides of the fence will be constructed with wire fencing at a cost of $2 per linear foot. The fourth side will be constructed with wood fenc- ing at a cost of $6 per linear foot. Find the dimensions and the area of the largest garden that can be enclosed with $320 worth of fencing. Example 2: Minimizing Perimeter Refer to Example 1. The homeowner judges that an area of 800 square feet for the garden is too small and decides to increase the area to 1,250 square feet. What is the minimum cost of building a fence that will enclose a garden with an area of 1,250 square feet? What are the dimensions of this gar- den? Assume that the cost of fencing remains unchanged.Example 3: Maximizing Revenue An office supply company sells x permanent markers per year at $p per marker. The pricedemand equation for these markers is p = 10 0.00M. What price should the company charge for the markers to maximize revenue? What is the maximum revenue? Example 4: Maximizing Prot The total annual cost of manufacturing .1: permanent markers for the ofce supply company in Example 3 is C(x) = 5,000 + 2.1: What is the company's maximum profit? What should the company charge for each marker, and how many markers should he produced? Example 5: Maximizing Prot The government decides to tax the company in Example 4 $2 for each marker produced. Taking into account this additional cost, how many markers should the company manufacture each week to maximize its weekly prot? What is the maximum weekly prot? How much should the company charge for the markers to realize the maximum weekly profit? Exam ale 6: Maximizing Revenue When a management training company prices its seminar on management techniques at $400 per person, 1.000 people will attend the sem- inar. The company estimates that for each $5 reduction in price. an additional 20 people will attend the seminar. How much should the company charge for the seminar in order to maximize its revenue? What is the maximum revenue