Question

Fabio and Gwen are saving money to buy a new gaming station. They need at least $510 to purchase the new gaming station. Gwen weeds yards and Fabio walks dogs to raise money. Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog. The number of dog walks that Fabio has scheduled is no more than twice the number of yards Gwen has scheduled to weed. Fabio will walk at least 25 dogs. Write a set of constraints to model the problem, with x representing the number of lawns weeded and y representing the number of dogs walked.

Answer 1

`12x + 9y \geq = 510\\ y\leq 2x\\ y \geq 25`

Explanation:

If x represents the number of lawns and 'y' represents the number of dogs that Fabio walked then:

The amount of money raised by Fabio plus the amount of money raised by Gwen must be greater than or equal to $ 510.

`12x + 9y \geq = 510`

The number of dogs that Fabio will walk is less than or equal to twice the number of yards of lawn cleared by Gwen.

`y\leq 2x`

Fabio will walk at least 25 dogs

`y \geq 25`

Finally, the restrictions are:

`12x + 9y \geq = 510\\ y\leq 2x\\ y \geq 25`