Modeling with Linear Systems Answers

Let x represent the number of chairs and y represent the number of sofas. Choose the function that represents the manufacturer’s profit, P.

Use the objective function P = 50x + 80y to calculate the profit at each point.(0, 5) P =

(1, 12) P =

(4, 10) P =

(0, 0) P =

(0, 15) P =

(6, 12) P =

$

The manufacturer can earn a maximum profit of by producing chairs and sofas.

The manufacturer can earn a maximum profit of by producing chairs and sofas.

The objective function is C = x + y.

The objective function is C = x + y.

The minimum cost is $ and occurs at .

The minimum cost is $ and occurs at .

Suppose you have $16,000 to invest in three stocks, A, B, and C. Stock A is a low-risk stock that has expected returns of 4%. Stock B is a medium-risk stock that has expected returns of 5%. Stock C is a high-risk stock that has expected returns of 6%. You want to invest at least $1,000 in each stock. To balance the risks, you decide to invest no more than $7,000 in stock C and to limit the amount invested in C to less than 4 times the amount invested in stock A. You also decide to invest less than twice as much in stock B as in stock A. How much should you invest in each stock to maximize your expected profit? Complete the constraints.Stock A: x Stock B: y and y x Stock C: 16 – x – y 16 – x – y 16 – x – y x

Which graph shows the feasible region for constraints x 1; y 1; y 2x; y –x + 15; y –5x + 16; and y –x + 9?

What are the vertices of the feasible region? Select four options..

Evaluate the profit function at each vertex.P = 0.04x + 0.05y + 0.06(16 – x – y) (8, 1) P =

(14, 1) P =

(3, 6) P =