Instructions: Use the given information to answer the questions and interpret key features. Use any method of graphing or solving.The roots of the quadratic function describing the relationship between number of products produced and overall profit margin are x=0𝑥=0 and 2828. The vertex is a minimum at (14,−40)(14,−40).The company actually loses money on their first few products as it costs them more to make them, but once they hit items they break even again.The worst case scenario is that they produce items, as they will have a profit of dollars. The first root tells us that the profit will be 00 when products are sold.

Instructions: For the following real-world problem, solve using any method. Use what you’ve learned to determine which method would be best. Put your answer in the context of the problem and determine the appropriate final answer.A business uses the following quadratic to model their profits where x𝑥 is number of products sold, in thousands: −x2+14x+94=0−𝑥2+14𝑥+94=0. Once they get to a certain number of products created, they no longer make a profit because of how taxing it is on their factories. Solve the quadratic to find the number of products that will cause them to no longer make a profit.What are the two solutions in exact form? x=𝑥= +√+ or −√− .What are the rounded values (to two decimal places)? or .Which of these answers makes sense in context to be the value of the number of products? x=𝑥=

Multiple Choice QuestionDuring the period, a company reports Sales of $38,000, Cost of Goods Sold of $20,000, and Income of $1,500. Profit margin is:Multiple choice question.3.9%8.3%7.5%

If a product has a selling price of $10, a contribution margin of $6 and fixed costs of $12 000, to make a profit of $36 000, the number of units that must be sold is:Group of answer choices4800.8000.12 000.2000.

If sales = $455,000, purchases = $225,000, beginning inventory = $150,000 and ending inventory = $118,000, gross profit is:$198,000$230,000$75,000$257,000

A small regional retailer is looking for ways to increase profits. Given its impressive record of growth, the sales and marketing vice president wants to target a 8% increase in sales to meet the profitability goals. The company currently has revenues of $34,000,000 (annually), spends 50% of its revenues on purchases, and has a net profit margin of 2.75%.You are a buyer working for this company and you want to show the vice president that it may be easier to reach the profitability goals by lowering purchasing expenses.If the company achieves its revenue growth target of 8%, by how many dollars would revenue increase? (Display your answer as a whole number.)   Assuming that revenues stayed flat (meaning the company did not try to increase sales by the 8 percent target), by what percentage would they have to decrease purchasing expenses to equal the increased profit that would have come from a 8 percent increase to revenues? (Write your answer as a percentage, and display your answer to two decimal places.)   %Note:  This question is to stretch your mind a bit and to show how much more, on a percentage basis, sales must increase in order to equal the bottom-line benefits of a modest decrease in purchasing expenses. There will not be a question like this on any assessment.The sales increase targeted percentage is _____ (how many) times bigger than the required percentage decrease in purchasing expenses. (Display your answer as a whole number.)