Mythology

Help me solve a linear programming word problem?

A factory manufactures two kinds of ceramic figurines: a fairy, and a mermaid, each requiring three process- molding, painting, and glazing. The daily labor available for molding is no more than 90 work-hours, labor available for painting does not exceed 120 work-hours, and labor available for glazing is no more than 60 work-hours. The fairy requires 3 work-hours for molding, 6 work-hours for painting, and 2 work-hours for glazing. The mermaid requires 3 work-hours for molding, 4 work-hours for painting, and 3 work-hours for glazing. If the profit on each figurine is $25 for fairies and $30 for mermaids, how many of each kind should be produced each day to maximize profit? What is the maximum profit?

I honestly don’t know how to do this and my notes just aren’t helping.T_T

Please help!

1. Identify the objective function
2. Identify the constraints

let x by number of fairies, let y be number of mermaids

1. Objective function:

P = 25x +30y

2. Constraints:

3x + 3y <= 90
6x + 4y <= 120
2x + 3y <= 60

Just graph the constraints and find the values for each corner point.

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