A manufacturer makes two products ,laptops bags and briefcases. Each must be processed through two work areas. Work are #1 has 50 hours of available production time each week. Work area #2 has 60 hours of available production time each week. Manufacturing of a laptop bag requires 3 hours in work area #1 and 2 hours in work area #2. Manufacturing of a briefcase requires 1 hours in work area #1 and 4 hours in work area #2. Profit is $6 per laptop $9 per window.a) Define decision variables that will tell how many units to build (laptops bags and briefcases) per week.b) Develop an objective function that will maximize profits per weekc) Develop production constraints for work area #1 and #2.d). What is the optimal solutions.

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Asked Feb 12, 2019
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A manufacturer makes two products ,laptops bags and briefcases. Each must be processed through two work areas. Work are #1 has 50 hours of available production time each week. Work area #2 has 60 hours of available production time each week. Manufacturing of a laptop bag requires 3 hours in work area #1 and 2 hours in work area #2. Manufacturing of a briefcase requires 1 hours in work area #1 and 4 hours in work area #2. Profit is $6 per laptop $9 per window.

a) Define decision variables that will tell how many units to build (laptops bags and briefcases) per week.
b) Develop an objective function that will maximize profits per week
c) Develop production constraints for work area #1 and #2.
d). What is the optimal solutions.

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Expert Answer

Step 1

Let us assume that L laptop bags and B briefcases are manufactured. These form the decision variables answering the part.

The objective function is given as below:

Maximize Profit per week, Z = 6L + 9B

The production constraint for work area #1 is given by:

3L + B <= 50 hours

The production constraint for work area #2 is given by:

2L + 4B <= 60 hours

The non-negativity constraints are given by L>=0 B>=0

Step 2

Solving the LP model using an LP solver such as MS-EXCEL ® we get the solution as:

Number o...

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