## Practice questions

**Given the function,**which of the following expressions is equivalent to

**What is the maximum value of***P*= 2*x*+ 5*y*subject to the constraints**A.**3.5**B.**8.75**C.**12**D.**12.25**E.**14

## Answers and explanations

**The correct answer is C.**Find

and simplify.

**The correct answer is C.**The three constraint inequalities define a region in the

*xy*-plane that represents their intersections. The region's boundary equations are*x*=*y*, 3*x*–*y*= 1, and 3*x*+*y*= 5. The maximum value of*P*will occur at one of the intersections of these three linear equations. To find the maximum value of*P*, systematically pair the three equations and solve for their intersections. Solving*x*=*y*and 3*x*–*y*= 1 by substitution yieldsThus, the intersection of

*x*=*y*and 3*x*–*y*= 1 isSolving

*x*=*y*and 3*x*+*y*= 5 by substitution yieldsThus, the intersection of

*x*=*y*and 3*x*+*y*= 5 isSolving 3

*x*–*y*= 1 and 3*x*+*y*= 5 by elimination yieldsThus, the intersection of 3

*x*–*y*= 1 and 3*x*+*y*= 5 is (1,2). Substitute the intersection points into*P*= 2*x*+ 5*y*to find the maximum:Therefore, subject to the given constraints, the maximum value of

*P*is 12, which occurs at (1,2).