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17 Sep 2020

A toy manufacturer can produce boxes of toys at a rate of . Find the total number of boxes the company can produce in .

Booster class
AP Calculus BC
Skill
Use accumulation functions and definite integrals in applied contexts
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A toy manufacturer can produce boxes of toys at a rate of . What is the total number of boxes the company can produce in ?

Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners

and bending up the sides. Find the largest volume that such a box can have.

  1. Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volumes of several such boxes. Does it appear that there is a maximum volume? If so, estimate it.

  2. Draw a diagram illustrating the general situation. Introduce notation and label the diagram with your symbols.

  3. Write an expression for the volume.

  4. Use the given information to write an equation that relates the variables.

  5. Use part (d) to write the volume as a function of one variable.

  6. Finish solving the problem and compare the answer with your estimate in part (a).

Cayden and Jayden had a total of $784. After Cayden spent 1/6 of his money on food and Jayden spent $124 on toys, they had the same amount left. How much money did Cayden have at first?

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