A craftswoman produces two products: floor lamps and table lamps. Production of one
floor lamp requires 75 minutes of her labor and materials that cost P250. Production of
one table lamp requires 50 minutes of labor, and the materials cost P200. The
craftswoman wishes to work no more than 40 hours each week, and her financial
resources allow her to pay no more than P9,000 for materials each week. She can sell
as many lamps as she can make and her profit is P390 per floor lamp and P330 per
table lamp.
1. Identify the variables.
2. Set up the objective function.
3. Give the constraints in mathematical expression.
4. Graph the constraints and identify the solution.
5. How many floor lamps and how many table lamps should she make each week to
maximize her weekly profit?
6. What is that maximum profit per week?
Answers
Given : A craftswoman produces two products: floor lamps and table lamps.
Production of one floor lamp requires 75 minutes of her labor and materials that cost P250.
Production of one table lamp requires 50 minutes of labor, and the materials cost P200.
The craftswoman wishes to work no more than 40 hours each week, and her financial resources allow her to pay no more than P9,000 for materials each week.
She can sell as many lamps as she can make and her profit is P390 per floor lamp and P330 per table lamp.
To Find :
How many floor lamps and how many table lamps should she make each week to maximize her weekly profit?
What is that maximum profit per week?
Solution:
floor lamps = F
Table Lamp = T
F , T ≥ 0
75F + 50T ≤ (40)(60)
=> 3F + 2T ≤ 96
250F + 200T ≤ 9,000
=> 5F + 4T ≤ 180
Profit = 390F + 330T
From Graph
T F Profit
0 32 12,480
30 12 14,580
45 0 14,850
Maximum Profit = 14850 when 45 Table Lamp
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