Solve the Following Problem Graphically $\operatorname { Max } \quad\quad\quad 5 \mathrm { X } + 6 \mathrm { Y }$

question 24

Essay

Solve the following problem graphically. $\operatorname { Max } \quad\quad\quad 5 \mathrm { X } + 6 \mathrm { Y }$
s.t. $\quad\quad\quad17 \mathrm { X } + 8 \mathrm { Y } \leq 136$
$\quad\quad\quad\quad3 \mathrm { X } + 4 \mathrm { Y } \leq 36$
$\quad\quad\quad\mathrm { X } , \mathrm { Y } \geq 0$ and integer
a.Graph the constraints for this problem.Indicate all feasible solutions.
b.Find the optimal solution to the LP Relaxation.Round down to find a feasible integer solution.Is this solution optimal?
c.Find the optimal solution.

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Definitions:

Predetermined Overhead Rate

A rate used in cost accounting to allocate overhead costs based on an estimated activity level.

Direct Labor-hours

The hours that workers contribute directly towards the manufacture of goods over a specified period.

Fixed Manufacturing Overhead

Costs associated with production that do not vary with the level of output, such as depreciation of machinery and the salary of the factory manager.

Job Cost

The total cost of labor, materials, and overhead allocated to a specific job or project.