29. The revenue generated by selling these bagels is the product of the price p times the number of bagels sold, x. Write anequation that represents revenue by substituting your result from above into the equation R = xp.30. The costs of doing business for a company can be found by adding fixed costs, such as rent, insurance, and wages,and variable costs, which are the costs to purchase the product you are selling. The portion of the bagel shop's fixedweekly costs allotted to bagels is $200, and the supplies to actually produce each bagel cost $0.75. Write an equationthat represents the total cost to the shop of producing x bagels. Your equation should look like C = mx + b.31. The profit made by the sale of these bagels is found by subtracting the costs from the revenue: P = R - C. Find anequation that represents profit by substituting your expressions for R and C into the profit formula. Simplify youranswer.2000 OR32. What is the profit made by selling 300 bagels each week?33. What is the profit made by selling 450 bagels each week? For Questions 28-37, refer to the following: From years of experience, a bagelshop has determined that at a price of p = $2.50, they will sell x = 450 bagelseach week. If they lower the price to p = $2.00, they will sell x = 550 bagelseach week.28. Assuming this relationship is linear, write an equation that relates theprice, p, to the number of bagels, x, that will be sold. Your equationshould look like p = mx + b.

Part 28 Let x,p be the point that represents x bagels sold each week at a price of $p. For p=$2.50, the sold bagels is x=450. For p=$2.00, the sold bagels is x=550. So, the points on the line are 450, 2.50 , 550, 2. The equation of the line through x1, y1 , x2, y2 is y-y2=y2-y1x2-x1x-x2. So, the linear equation through 450, 2.50 , 550, 2 is: p-2=2-2.50550-450x-550⇒p=-0.50100x-550+2⇒p=-0.005x+4.75 So, the equation is p=-0.005x+4.75.Part 29 The revenue is : R=xp=x-0.005x+4.75=-0.005x2+4.75x So, the revenue is R=-0.005x2+4.75x.Part 30 The cost of each bagel is $0.75. So, the cost of x bagels is 0.75x. The fixed cost is $200. So, the total cost is: C=0.75x+200Part 31 The profit is: P=R-C=-0.005x2+4.75x-0.75x+200=-0.005x2+4x-200 So, the profit is P=-0.005x2+4x-200. Part 32 The profit is P=-0.005x2+4x-200 for x bagels each week. So, for 300 bagels each week, the profit is: P=-0.0053002+4300-200=550 So, the profit for 300 bagels is $550 . Part 33 The profit is P=-0.005x2+4x-200 for x bagels each week. So, for 450 bagels each week, the profit is: P=-0.0054502+4450-200=587.5 So, the profit for 450 bagels is $587.5 . Answer: Part 28: the equation is p=-0.005x+4.75. Part 29: The revenue is R=-0.005x2+4.75x. Part 30: The total cost is C=0.75x+200. Part 31: The profit is P=-0.005x2+4x-200. Part 32: The profit for 300 bagels is $550 . Part 33: The profit for 450 bagels is $587.5 .