A manufacturer produces three models of bicycles. The times (in hours) required for assembling, painting, and packaging each model are shown in the table below: Model A Model B Model Assembling 2 2.5 3 Painting 1.5 2 1Packaging 1 0.75 1.25 The total time available for assembling is 4006 hours, for painting is 2495 hours, and for packaging is 1500 hours. The profits per unit are $45 for Model A. $50 for Model B and $55 for Model C. What is the optimal production level for each model, and what is the optimal profit? A) Set up the objective function. B) Set up the constraints in inequality form. C) Rewrite your answer to (b) as equations with slack variables. D) Write the initial tableau for solution via the simplex method.

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 0 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24

Mia’s gross pay is 2953 her deductions total 724.15 what percent if her gross pay is take-home pay