Linear Programming

[lilmiss2013]

The Sandu Dandy Dune Buggy Company makes two models of off-road vehicles: The Sand crab and the Surf mobile. They can get the basic parts to produce as many as 15 sand crabs and 12 surf mobiles per a week. Howeve, 2 parts have to be special ordered: a unique exhaust manifold clamp and a specially designed suspension joint. Each sand crab requires 5 manifold clamps and 2 suspension joints. Each surf mobile requires 3 manifold clamps and 6 suspension joints. Each surf mobile requires 3 manifold clamps and 6 suspension joints. For each week the maximum number of clamps available is 81 per a week and the maximum number of joints is 78 per a week. it takes 20 hours to assemble one sand crab and 30 hours to assemble on surf mobile. the company has 12 employees who each work a maximum of 37.5 hours per a week. your group has been hired as consultants to the company to advise them on how many sand crabs and how many surf mobiles they should make each week to maximize their profit. they know their profit margin on each sand crab in $500 and each surf mobile it is $1000.

I am having trouble with the inequalities and objective function for this problem.

 

[mmm4444bot]

I am having trouble with the inequalities and objective function for this problem.

Did you decide to use x for the number of sand crabs and y for the number of surf mobiles?

Try to fill in the "blanks" below.

The objective is to make as much money as possible. So, the objective function is a profit function.

You can write an expression for the profit function, yes? They tell us how much profit is made on each x and how much profit is made on each y. (Read the last sentence.)

P(x, y) = ? x + ? y

So, near the end of our work, this is the function into which we will substitute the (x, y) values at the intersection points of the solution region's boundary lines.

?

They can get the basic parts to produce as many as 15 sand crabs and 12 surf mobiles per a week.

This tells us the limits on x and y.

? ? x ? ?

? ? y ? ?

?

Each sand crab requires 5 clamps
Each surf mobile requires 3 clamps
the maximum number of clamps available is 81

This tells us how to model the limit on the clamps.

? x + ? y ? 81

?

Each sand crab requires 2 joints
Each surf mobile requires 6 joints
the maximum number of joints available is 78

This tells us how to account for the limit on the joints.

? x + ? y ? ?

So, that's four lines, so far.

The last one involves the constraint on the hours.

Look for the given information. How many total hours are available from 12 people working 37.5 hours each?

How many hours are needed for x? For y?

Write the inequality.

? x + ? y ? ?

That's it. Now you're ready to find the vertex points. (There's six, ignoring the Origin.)

Test those six pairs of (x, y) values in the function P(x, y), to see which one generates the most money.

Cheers ~ Mark