Exam 5: Systems of Equations and Inequalities

A mixture of 5 gallons of chemical A, 6 gallons of chemical B, and 22 gallons of chemical C is required to kill a crop destroying insect.Commercial spray X contains 1, 2, and 3 parts of these chemicals, respectively.Commercial spray Y contains only chemical C.Commercial spray Z contains chemicals A, B, and C in equal amounts.How much of commercial spray is needed to obtain the desired mixture?

Solve the system by the method of elimination.

A chemist needs 20 liters of a 45% acid solution.The solution is to be mixed from three solutions whose acid concentrations are 10%, 20%, and 50%.How many liters of the 50% solution should the chemist use if trying to use as little as possible of the 50% solution?

Which of the following vertices of the constraint region shown is a maximum value of the objective function below.

Write an inequality for the shaded region shown in the figure.

An accounting firm charges $2500 for an audit and $350 for a tax return.Research and available resources have indicated the following constraints. The firm has 900 hours of staff time available each week. The firm has 155 hours of review time available each week. Each audit requires 75 hours of staff time and 10 hours of review time. Each tax return requires 12.5 hours of staff time and 2.5 hours of review time. What numbers of audits and tax returns will bring in an optimal revenue?

Determine whether the system of equations below has one solution, two solutions, or no solution.

You are offered two different jobs.Company A offers an annual salary of $34,000 plus a year-end bonus of 3.5% of your total sales.Company B offers a salary of $28,000 plus a year-end bonus of 7.5% of your total sales.What is the amount you must sell in one year to earn the same salary working for either company?

Solve the system of linear equations.

Solve the system of equations below:

Solve the system by the method of elimination.

The costs to a store two models of Global Positioning System (GPS) receivers are $80 and $100.The $80 model yields a profit of $25 and the $100 model yields a profit of $30.Market tests and available resources indicate the following constraints. The merchant estimates that the total monthly demand will not be exceed 200 units. The merchant does not want to invest more than $18,000 in GPS receiver inventory. What is the optimal inventory level for each model what is optimal profit?

Find the equilibrium point of the demand and supply equations.(The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply P = 36 - 0.02x p = 0.5x - 380

A company makes two types of telephone answering machines: the standard model and the deluxe model.Each machine passes through three processes: and One standard answering machine requires 2 hours in 5 hours in and 3 hours in One deluxe answering machine requires 3 hours in 5 hours in and 1 hour in Because of employee work schedules, is available for 30 hours, is available for 55 hours, and is available for 27 hours.If the profit is $47 for each standard model and $28 for each deluxe model, how many units of each type should the company produce to maximize profit?

Solve each system of equations by the substitution method.

A humanitarian agency can use two models of vehicles for a refugee rescue mission.Each model A vehicle costs $1000 and each model B vehicle costs $1500.Mission strategies and objectives indicate the following constraints. A total of at least 20 vehicles must be used. A model A vehicle can hold 45 boxes of supplies.A model B vehicle can hold 30 boxes of supplies.The agency must deliver at least 690 boxes of supplies to the refugee camp. A model A vehicle can hold 20 refugees.A model B vehicle can hold 32 refugees.The agency must rescue at least 520 refugees. What is the optimal number of vehicles of each model that should be used? What is the optimal cost?

Determine which ordered pair is a solution of the system.

The supply and demand equations for a small LCD television are given by where is the price (in dollars) and represents the number of televisions.For how many units will the quantity demanded equal the quantity supplied? What price corresponds to this value?

Write a system of inequalities whose solution set is graphed below.

Find the equation of the parabola that passes through the points.