Exam 7: Linear Programming

A manufacturing company wants to maximize profits on products $A, B$ , and $C$ . The profit margin is $\$ 3$ for $A, \$ 6$ for $B$ , and $\$ 15$ for $C$ . The production requirements and departmental capacities are as follows: -What is the maximum profit in this model?

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24rings each day using up to 60 total man hours of labor. It takes 3 man hours to make one VIP ring, versus 2 man hoursto make one SST ring. -How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $\$ 50$ and on an SST ring is $\$ 10$ ?

Provide an appropriate response. -If a system has four inequalities, the number of corner points of the feasible region must be ?

A manufacturer of wooden chairs and tables must decide in advance how many of each item will be made in a givenweek. Use the table to find the system of inequalities that describes the manufacturer's weekly production. -Use $x$ for the number of chairs and $y$ for the number of tables made per week. The number of work-hours available for construction and finishing is fixed.

Use the two-stage method to solve. -Find $x_{1} \geq 0$ and $x_{2} \geq 0$ such that $3 x_{1}+3 x_{2} \geq 60$ $2 x_{1}+5 x_{2} \leq 120$ And $z=5 x_{1}+4 x_{2}$ is maximized.

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24rings each day using up to 60 total man hours of labor. It takes 3 man hours to make one VIP ring, versus 2 man hoursto make one SST ring. -How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $\$ 50$ and on an SST ring is $\$ 40$ ?

Find the pivot in the tableau. -

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24rings each day using up to 60 total man hours of labor. It takes 3 man hours to make one VIP ring, versus 2 man hoursto make one SST ring. -How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $\$ 30$ and on an SST ring is $\$ 60$ ?

Use the two-stage method to solve. -Maximize $\mathrm{z}=3 \mathrm{x}_{1}+2 \mathrm{x}_{2}$ Subject to: $\mathrm{x}_{1}+\mathrm{x}_{2}=5$ $4 \mathrm{x}_{1}+2 \mathrm{x}_{2} \geq 12$ $5 x_{1}+2 x_{2} \leq 16$ $x_{1} \geq 0, x_{2} \geq 0$

Find the transpose of the matrix. -

Use the two-stage method to solve. -Find $x_{1} \geq 0$ and $x_{2} \geq 0$ such that +\leq50 +\geq25 2+\leq60 And $\mathrm{z}=3 \mathrm{x}_{1}+4 \mathrm{x}_{2}$ is maximized.

Find the value(s) of the function on the given feasible region. -Find the minimum of $z=23 x+14 y+19$ .

Provide an appropriate response. -To determine the shading when graphing $6 x+8 y \geq 0$ , the point $(0,0)$ would make a good test point. ?

Provide an appropriate response. -Each solution of a simplex tableau corresponds to

Find the pivot in the tableau. -

Use graphical methods to solve the linear programming problem. -Minimize $\quad z=0.18 x+0.12 y$ Subject to: $\quad 2 x+6 y \geq 30$ $4 x+2 y \geq 20$ $x \geq 0$ $y \geq 0$

Graph the linear inequality. - $x-y<6$

Solve the problem. -An appliance store sells two types of refrigerators. Each Cool-It refrigerator sells for $\$ 580$ and each Polar sells for $\$ 740$ . Up to 260 refrigerators can be stored in the warehouse and new refrigerators are delivered only once a month. It is known that customers will buy at least 60 Cool-Its and at least 140 Polars each month. How many of each brand should the store stock and sell each month to maximize revenues?

A manufacturing company wants to maximize profits on products $A, B$ , and $C$ . The profit margin is $\$ 3$ for $A, \$ 6$ for $B$ , and $\$ 15$ for $C$ . The production requirements and departmental capacities are as follows: -What are the coefficients of the objective function?

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24rings each day using up to 60 total man hours of labor. It takes 3 man hours to make one VIP ring, versus 2 man hoursto make one SST ring. -How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $\$ 40$ and on an SST ring is $\$ 35$ ?