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Answer:
a) Objective Function:
P = $18.6x + $13.9y
b)
1. 2x + 2.5y 3000 For Carpentry
2. 1.5x +1.0 y 1500 For Painting
3. 1.3x + 1.2y 1500 For Finishing
c)
x 500
y 650
Explanation:
Data Given:
Contemporary Style Cabinets Sells For = $90
Farmhouse Style Cabinets Sell For = $85
Hours per process:
For Contemporary:
Time for Carpentry = 2.0
Time for Painting = 1.5
Time for Finishing = 1.3
Similarly,
for Farmhouse Cabinet style:
Time for Carpentry = 2.5
Time for Painting = 1.0
Time for Finishing = 1.2
Costing for Processes:
Carpentry = $15/hr
Painting = $12/hr
Finishing = $18/hr
Availability of hours in the week:
Carpentry = 3000 hours
Painting = 1500 hours
Finishing = 1500 hours
Orders for Cabinets in the week:
Contemporary Cabinets = 500 units/week
Farmhouse Style = 650 units/week
Suppose,
x = number of contemporary style cabinets
y = number of Farmhouse cabinets
Step 1:
We need to calculate the total cost of the cabinets first.
Cost of Contemporary Style:
(2 x $15) + (1.5 x $12) + (1.3 x $18) = $71.4/cabinet
Similarly,
Cost of Farmhouse Style:
(2.5 x $15) + (1 x $12) + (1.2 x $18) = $71.1/cabinet
We know that the selling price of Contemporary and Farmhouse cabinets is $90 and $85 respectively. So, we can calculate the profit of both the cabinets.
For Contemporary Style:
Profit = ($90-$71.4) =$18.6
For Farmhouse Style:
Profit = ($85-$71.1)= $13.9
a) Objective Function for the maximization of the profit:
We know that x represents contemporary style and y represents farmhouse style. So, the profit is the basically the objective function. So.,
Objective Function:
P = $18.6x + $13.9y
b) Mathematical Expression for the constraints, which are:
1. 2x + 2.5y 3000 For Carpentry
2. 1.5x +1.0 y 1500 For Painting
3. 1.3x + 1.2y 1500 For Finishing
c) Mathematical Expression for Contracts:
x 500
y 650