find eqn for salary, for cost fcn; use slack vars to convert

[dcc3038026]

Having difficulties solving these 3 problems, can anybody please help? Thanks...

1. After two years on the job, an engineer's salary was $60,000. After seven years on the job, her salary was $72,500. Let y represent her salary after x years on the job. Assuming that the change in her salary over time can be approximated by a straight line, give an equation for this line in the form y = mx + b.

2. A book publisher found that the cost to produce 1000 calculus textbooks is $26,100, while the cost to produce 2000 calculus textbooks is $51,400. Assume that the cost C(x) is a linear function of x, the number of textbooks produced. What is the marginal cost of a calculus textbook?

3. Use slack variables to convert the constraints into linear equations.
Maximize z = 1.1x1 + 2.6x2
Subject to: 1.9x1 + 1.5x2? 48
1.6x1 + 1.3x2? 39
with: x1? 0, x2? 0

 

[stapel]

1. After two years on the job, an engineer's salary was $60,000. After seven years on the job, her salary was $72,500. Let y represent her salary after x years on the job. Assuming that the change in her salary over time can be approximated by a straight line, give an equation for this line in the form y = mx + b.

You are given two points (namely, s = 60000 when t = 2 and s = 72500 when t = 7) and are asked to find the equation of the line through the two points. So do what you learned back in pre-algebra or elementary algebra:

i) Plug the two points into the slope formula.
ii) Simplify to find the value of the slope.
iii) Pick one of the points. (It doesn't matter which one.)
iv) Plug the point and the slope into the line equation of your choice.
v) Solve for "y", simplifying to get "y = mx + b".

2. A book publisher found that the cost to produce 1000 calculus textbooks is $26,100, while the cost to produce 2000 calculus textbooks is $51,400. Assume that the cost C(x) is a linear function of x, the number of textbooks produced. What is the marginal cost of a calculus textbook?

This one works just like exercise (1).

3. Use slack variables to convert the constraints into linear equations.
Maximize z = 1.1x1 + 2.6x2
Subject to: 1.9x1 + 1.5x2? 48
1.6x1 + 1.3x2? 39
with: x1? 0, x2? 0

This is on an entirely different level from the other exercises, being a process from optimization techniques (or perhaps more-advanced linear algebra). If you don't know how to get started on (1) or (2), I'm afraid I can't imagine how even to begin to explain (3). Sorry!

Eliz.

 

[dcc3038026]

Yes, I understand about exercise number (3) being a different level and I am too embararred to ask but I have this as a homework assignment and need help with a soluation, can you work it as an example and maybe I could use it as a tool for learning??? I can handle exercise (1) & (2).
Thanks,

 

[Denis]

3. Use slack variables to convert the constraints into linear equations.
Maximize z = 1.1x1 + 2.6x2
Subject to: 1.9x1 + 1.5x2? 48
1.6x1 + 1.3x2? 39
with: x1? 0, x2? 0

Bad idea to use stuff like x1 and x2 as variables: only ends up in confusion; make a=x1 and b=x2;
also good idea to get rid of decimals: with your problem, multiply each term by 10:

Maximize z = 11a + 26b
Subject to: 19a + 15b ? 480
16a + 13b ? 390
with: a ? 0, b ? 0

Did you click on Stapel's link she gave you as "explain" ?

 

[dcc3038026]

Yeah, I reviewed the link "explain" supplied by Stapel but I still continue to have problems, could you work this one as an example for me to use as a learning tool?
Thanks,
Dcc

 

[stapel]

I reviewed the link...but I still continue to have problems, could you work this one as an example for me to use as a learning tool?

If all of the worked examples in your textbook, in your class notes, and in the various different online articles you studied have left you still unable to get started (which is reasonable, considering that you're also having trouble with material typically covered years earlier in college study), then one more example is of course highly unlikely to lead suddenly to complete understanding. :shock:

So hiring a tutor and setting aside an hour or two a day for the next few months (or enrolling in an appropriate sequence of courses at your local college or university) may be your best bet -- if you truly have no understanding of this material and are unable to make any start on this exercise -- as we obviously cannot here provide the semesters of material necessary to take you from pre-algebra or elementary-algebra topics to what you need to know. Sorry!

If, on the other hand, you exaggerated your degree of "lostness" and you were in fact able to make some start, please reply with a clear and complete listing of your work and reasoning so far, so that we can at least attempt to find lessons for you that cover specific topics that might prove helpful. :idea:

Thank you!

Eliz.