Linear Algebra – Homework # 2

1.)Many Americans love to eat fast food. But we are also concerned about weight gain and the cholesterol that is generated by eating saturated fat. Many fast-food restaurants now advertise special “lite” menus. They give information about the fat and calorie content of those foods, like the data in the following table.

Item / Grams Fat / Total Calories / Calories from Fat
McDonald’s
McLean Deluxe / 12 / 350 / 150
Fillet O’ Fish / 16 / 360 / 150
McLean Deluxe & Small Fries / 22 / 560 / 200
KFC
Skinfree Crispy Breast / 17 / 293 / 153
Chicken Sandwich / 27 / 482 / 243
Wendy’s
Chicken Sandwich / 20 / 450 / 180
Baked Potato with Broccoli & Cheese / 14 / 460 / 120
Taco Salad / 30 / 580 / 270
Hardee’s
Fisherman’s Fillet / 20 / 450 / 180
Grilled Chicken Sandwich / 9 / 290 / 80

a.)Make a scatterplot of the data relating grams of fat F to total calories T in the menu items shown. You may do this on your graphing calculator, however, you will also need to draw the graph on the attached graph paper.

b.)Draw a linear model joining the points (12, 350) and (30, 580). Find the equation in the form y = mx + b or T = mF + b. Explain what the values of m and b tell you about the relationship between the grams of fat and the total calories in the food items.

c.)Use your graphing calculator to find the linear regression model for the (F, T) data in the table. Compare this equation to the one you found in part b. Write at least one statement describing how these two equations compare.

2.)Bronco Electronics is a regional distributer of graphing calculators. When an order is received, a shipping company packs the calculators in a box. They place the box on a scale which automatically finds the shipping cost. The cost C is a function of the number of calculators N in the box using the rule

C = 4.95 + 1.25N.

a.) Write an equation or inequality that could be used to answer the following questions. Then use a table or a graph (either generated by hand or with a calculator) or some other method to answer the questions.

  • If the shipping cost is $17.45, how many calculators are in the box?
  • How many calculators can be shipped if the cost is to be held below $25?
  • What is the cost of shipping eight calculators?

b.)What questions about shipping costs could be answered using the following equation and inequality?

  • 27.45 = 4.95 + 1.25N
  • 4.95 +1.25N < 10

c.)Bronco Electronics got an offer from a different shipping company. The new company would charge based on the rule C = 7.45 + 1.00N. Write and solve equations or inequalities to answer the following questions (again, you can use a table or a graph or another method if you prefer.)

  • For what number of calculators in a box will the two shippers make the same charge?
  • For what number of calculators in a box will the new shipping company’s offer be more economical for Bronco Electronics?