Question

christy uses glass beads to make braclets and necklances it takes her 30 minutes to make a bracelet and 45 minites to make a necklace she works at.most 40 hours she wants to make atleast 30 bracelts the profit from the bracelets os $10 and the profit from a necklace is 18 determine make to maximize her.profit show your work compare the solution of a system of linear inequalities and the solution to an equation calculated by linear program

Answer 1

Christy should make at least 30 bracelets and at most 40 necklaces to maximize profit

How to determine how many bead of each type of bracelets and necklaces should Christy make to maximize his​ profit?

The given parameters can be represented in the following tabular form:

                       Bracelet (x)    Necklace (y)    Total              

Labor (hour)        0.5                       0.75         40

Profit                    10                         18

From the above table, we have the following:

Objective function:

Max P = 10x + 18y

Subject to:

0.5x + 0.75y <= 40

Because she wants to make at least 30 bracelets, we have:

x >= 30

So, we have:

Max P = 10x + 18y

Subject to:

0.5x + 0.75y <= 40

x >= 30

Express x >= 30 as equation

x = 30

Substitute x = 30 in 0.5x + 0.75y <= 40

0.5 * 30 + 0.75y <= 40

This gives

15 + 0.75y <= 40

Subtract 15 from both sides

0.75y <= 30

Divide by 0.75

y <= 40

Hence, Christy should make at least 30 bracelets and at most 40 necklaces to maximize profit

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