Applications Involving Inequalities

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Presentation transcript:

Applications Involving Inequalities Our last “new” stuff of the chapter!!! 2.9c

Designing a Box – Revisited!!! Dixie Packaging Company has contracted with another firm to design boxes with a volume of at least 600 cu. in. Squares are still to be cut from the corners of a 20-in. by 25-in. piece of cardboard, with the flaps folded up to make an open box. What size squares should be cut from the cardboard? Do you recall the diagram??? The equation for the volume??? We need a volume of at least 600: Solve graphically!!! Squares with side lengths between 1.659 in. and 6.159 in. (inclusive) will produce a volume of 600 cu. in. or greater.

Designing a Juice Can – Revisited!!! Stewart Cannery will package tomato juice in 2-liter cylindrical cans. Find the radius and height of the cans if the cans have a surface area that is less than 1000 square centimeters. Do you recall the equations for volume and surface area??? The inequality to be solved: Solve graphically!!!

Designing a Juice Can – Revisited!!! Stewart Cannery will package tomato juice in 2-liter cylindrical cans. Find the radius and height of the cans if the cans have a surface area that is less than 1000 square centimeters. To find the height, let’s solve a double inequality:

Designing a Juice Can – Revisited!!! Stewart Cannery will package tomato juice in 2-liter cylindrical cans. Find the radius and height of the cans if the cans have a surface area that is less than 1000 square centimeters. To find the height, let’s solve a double inequality: The surface area of the can will be less than 1000 sq. cm. if its radius is between 4.619 cm and 9.655 cm and its height is between 6.829 cm and 29.839 cm.

The electrician worked no more than 4 hours. More Practice Problems Pederson Electric Co. charges $25 per service call plus $18 per hour for home repair work. How long did an electrician work if the charge was less than $100? Assume the electrician rounds off time to the nearest quarter hour. Let x be the number of hours worked Repair charge: , which must be less than $100: The electrician worked no more than 4 hours.

The company needs to sell 9091 candy bars to make a profit More Practice Problems A candy company finds that the cost of making a certain candy bar is $0.13 per bar. Fixed costs amount to $2000 per week. If each bar sells for $0.35, find the minimum number of candy bars that will earn the company a profit. Let x be the number of candy bars made Costs: Income: Need income to be greater than costs: The company needs to sell 9091 candy bars to make a profit

More Practice Problems The total electrical resistance R of two resistors connected in parallel with resistances R and R is given by 1 2 One resistor has a resistance of 2.3 ohms. Let x be the resistance of the second resistor. (a) Express the total resistance R as a function of x.

More Practice Problems The total electrical resistance R of two resistors connected in parallel with resistances R and R is given by 1 2 One resistor has a resistance of 2.3 ohms. Let x be the resistance of the second resistor. (b) Find the resistance in the second resistor if the total resistance of the pair is at least 1.7 ohms.

The resistance of the second resistor is at least 6.517 ohms More Practice Problems The total electrical resistance R of two resistors connected in parallel with resistances R and R is given by 1 2 One resistor has a resistance of 2.3 ohms. Let x be the resistance of the second resistor. (b) Find the resistance in the second resistor if the total resistance of the pair is at least 1.7 ohms. Where is this function greater than or equal to zero? Check the graph! The resistance of the second resistor is at least 6.517 ohms