Ice Cream The Mom and Pop Ice Cream Company makes two kinds of chocolate ice cream: regular and premium. The properties of 1 gallon (gal) of each type are shown in the table:
In addition, current commitments require the company to make at least 1 gal of premium for every 4 gal of regular. Each day, the company has available 725 pounds (lb) of flavoring and 425 lb of milk-fat products. If the company can ship no more than 3000 lb of product per day, how many gallons of each type should be produced daily to maximize profit?
Source: www.scitoys.com/ingredients/ice_cream.html
Want to see the full answer?
Check out a sample textbook solutionChapter 11 Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus and Its Applications (11th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Calculus: Early Transcendentals (3rd Edition)
- A 16-ounee chocolate mocha coffee with whipped cream contains 470 calories, 18 grams of fat, 63 grams of carbohydrates, and 15 grams of protein. Find the unit rate of (a) calories per ounce (b) grams of fat per ounce (c) grams of carbohydrates per ounce (d) grams of protein per ounce.arrow_forwardCholesterol Cholesterol in human blood is necessary, but too much can lead to health problems. There are three main types of cholesterol: HDL (high-density lipoproteins), LDL (low-density lipoproteins), and VLDL (very low-density lipoproteins). HDL is considered “good” cholesterol; LDL and VLDL are considered “bad” cholesterol. A standard fasting cholesterol blood test measures total cholesterol, HDL cholesterol, and triglycerides. These numbers are used to estimate LDL and VLDL, which are difficult to measure directly. Your doctor recommends that your combined LDL/VLDL cholesterol level be less than 130 milligrams per deciliter, your HDL cholesterol level be at least 60 milligrams per deciliter, and your total cholesterol level be no more than 200 milligrams per deciliter. (a) Write a system of linear inequalities for the recommended cholesterol levels. Let x represent the HDL cholesterol level, and let y represent the combined LDL VLDL cholesterol level. (b) Graph the system of inequalities from part (a). Label any vertices of the solution region. (c) Is the following set of cholesterol levels within the recommendations? Explain. LDL/VLDL: 120 milligrams per deciliter HDL: 90 milligrams per deciliter Total: 210 milligrams per deciliter (d) Give an example of cholesterol levels in which the LDL/VLDL cholesterol level is too high but the HDL cholesterol level is acceptable. (e) Another recommendation is that the ratio of total cholesterol to HDL cholesterol be less than 4 (that is, less than 4 to 1). Identify a point in the solution region from part (b) that meets this recommendation, and explain why it meets the recommendation.arrow_forwardCicadas are flying, plant-eating insects. One species, the 13-year cicadas (Magicicada), spends five juvenile stages in underground burrows. During the 13 years underground, the cicadas grow from approximately the size of a small ant to nearly the size of an adult cicada. The adult body weights (BW) in grams and wing lengths (WL) in millimeters are given for three different species of these 13-year cicadas in the following table. It is of interest to determine if body weight is a significant predictor of wing length for a 13-year cicada. Considering all assumptions for a parametric test are satisfied, use the obtained jamovi © outputs below to answer the following: Test whether the wing length of 13-year cicadas is linearly dependent on its body weight at 5% level of significance.arrow_forward
- Cicadas are flying, plant-eating insects. One species, the 13-year cicadas (Magicicada), spends five juvenile stages in underground burrows. During the 13 years underground, the cicadas grow from approximately the size of a small ant to nearly the size of an adult cicada. The adult body weights (BW) in grams and wing lengths (WL) in millimeters are given for three different species of these 13-year cicadas in the following table. It is of interest to determine if body weight is a significant predictor of wing length for a 13-year cicada. Considering all assumptions for a parametric test are satisfied, use the obtained jamovi © outputs below to answer the following: Is it logical to proceed to simple linear regression? If yes, provide an estimate of the simple linear regression line. Specify which variables should be considered as the response and independent variable.arrow_forwardUse the given information to answer the following questions: Elizabeth’s Cranberry Chutney is available by the case for $59.88. Each case contains 12 jars. Each 10-fluid-ounce jar contains 12 ounces of chutney. A tablespoon of chutney weighs 0.6 ounce. a.How much will 1 tablespoon of chutney cost? b. What is the cost per ounce of chutney? c. If you need 2 cups of chutney to make a special salad, how much will the 2 cups cost? d. How much would a pound of chutney cost? 2. How much would 1 3/4 cups of milk cost if you purchase milk by the gallon for $3.39? 3. Bob bought 22 chickens. Each chicken weighs 3.5 pounds. The chickens cost Bob $99.33. How much did each chicken cost, and what is the cost per pound? 4. You purchase a case of dried cherries for $52.00. The case contains fourteen 12-ounce packages. What is the cost per pound? What is the cost per ounce? 5. You make 12 cakes for a total cost of $71.52. Each cake is to be cut into 12 portions. How much does each cake cost you to…arrow_forwardNicole started a new diet that requires each meal to have 340 calories, 6 grams of fiber, and 6 g of fat. The table shows the fiber, fat, and calorie content of one serving of each of three breakfast foods. How many servings of each food should Nicole eat to follow her diet? toast serving(s) cottage cheese serving(s) fruit serving(s) Food Fiber (g) Fat (g) Calories Toast 2 1 100 Cottage cheese 0 5 120 Fruit 2 0 60arrow_forward
- A food factory makes three types of cereals, A, B and C, from a mix of several ingredients: Oates, Apricots, Coconuts and Hazelnuts. The cereals are packaged in 2kg boxes. The following table provides details of the sales price per box of cereals and the production cost per ton (1000 kg) of cereals respectively. Sales price per box($) | Production cost per ton Cereal A 2.50 4.00 Cereal B Cereal C 2.00 2.80 3.50 3.00. The following table provides the purchase price per ton of ingredients and the maximum availability of the ingredients in tons respectively. |Ingredients Purchase price ($) per ton Maximum availability in tons Oates 100 10 Apricots Coconuts 120 80 Hazelnuts 200 2 The minimum daily demand (in boxes) for each cereal and the proportion of the Oates, Apricots, Coconut and Hazelnuts in each cereal is detailed in the following table, Proportion of Minimum demand (boxes) Oates | Apricots | Coconuts | Hazelnuts 0.05 Cereal A 1000 0.8 0.1 0.05 Cereal B Cereal C 700 0.65 0.2 0.05…arrow_forward1) A recipe calls for 1 1/2 gallons of chopped onions. How many pounds of onion should you use if one cup of chopped onions weighs 6.5 ounces? 2) You are making 8 chocolate cakes. Each cake requires 3/4 cup of cocoa powder. How many pounds of cocoa powder should you use if 1 tablespoon weighs 1/4 ounce? 3) You are making gingerbread cookies. The recipe calls for 1 1/2 kilograms of molasses. You purchase molasses in 16-fluid ounce containers. If one cup of molasses weighs 12 ounces, how many containers of molasses should you use? 4) You are making pumpkin soup. The recipe calls for 3 pounds of pumpkin purée. You cook and purée the pumpkin and measure out 8 cups of the purée. If one cup of pumpkin purée weighs 6 1/2 ounces, will you have enough pumpkin purée? If not, how much more will you need? If you have more than enough, how much will be left over? 5) You are calculating the yield percent for lettuce. You determine that the yield is 103%. How do you know that this is incorrect?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL