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Linear Programming Solution

## Assessment and Readiness Plan for the Plant

Use the information below, the attached linear programming solution, and the qdma solution video found in Canvas in Week 3 to interpret the linear program solution results and develop an assessment and readiness plan for the plant. Your assessment and readiness plan should be no more than 3 pages and may include additional appendices if needed, and should focus on the following:

-The market for the plant's products is in constant flux.  Input costs and product pricing can change throughout the planning period.  Evaluate the sensitivity of the solution to changes in profit contribution.  Note:  You do not need to tackle the revenue and cost sides separately from an analysis perspective. You can focus on overall profit contribution for each product.  However, your discussion should consider that changes in profit contribution may result from revenue changes or cost changes.

-Machine over- and under-utilization is always important.  Provide an assessment of current capacity for the 3 machines.  This should include a discussion of any current capacity constraint issues as well as potential opportunities for the use of unused machine capacity.  Note:  Disregard the sensitivity information provided for the 3 "equal to" constraints in the formulation and focus this analysis on the "less than or equal to" constraints which directly relate to machine utilization.

-Your assessment may also focus on any other aspect of the solution or sensitivity analysis that you find noteworthy.

Provide specific recommendations based on your analysis supported by the optimal solution to the program and the sensitivity analysis.  The recommendations may be opportunities or areas of concern that need to be closely monitored.A certain plant can manufacture five different products in any combination. Each product requires time on each of three machines in the following manner (figures in minutes/unit):

 1 2 3 12 8 5 7 9 10 8 4 7 10 0 3 7 11 2

Each machine is available 128 hours per week.Products A, B, and C are purely competitive and any amounts made may be sold at respective prices of \$5, \$4, and \$5. The first 20 units of D and E produced per week can be sold at \$4 each, but all made in excess of 20 can only be sold at \$3 each.  Variable labor costs are \$4 per hour for machines 1 and 2, while machine 3 labor costs \$3 per hour. Material costs are \$2 for products A and C, while products B, D, and E only cost \$1.You wish to maximize profit to the firm.

The principal complication is that the profit contributions of products D and E are not linear; the market price for the first 20 units differs than the market price for units produced above 20 units. We will define two additional products D2 and E2, which sell for \$3 per unit and set limits on the production of the original products D and E.

 Number of units of A produced per week 5 - 2 = \$3 Number of units of B produced per week 4 - 1 = \$3 Number of units of C produced per week 5 - 2 = \$3 Number of units of D not in excess of 20 produced per week 4 - 1 = \$3 Number of units of D in excess of 20 produced per week 3 - 1 = \$2 Number of units of E not in excess of 20 produced per week 4 - 1 = \$3 Number of units of E in excess of 20 produced per week 3 - 1 = \$2 Hours of machine 1 used per week -\$4 Hours of machine 2 used per week -\$4 Hours of machine 3 used per week -\$3 *Total production of product D is D + D2   Total production of product E is E + E2

MAX Profit = 3 * A + 3 * B + 3 * C + 3 * D + 2 * D2 + 3 * E + 2 * E2 - 4 * M1 - 4 * M2 - 3 * M3

12*A + 7*B + 8*C + 10*D + 10*D2 + 7*E + 7*E2 - 60*M1 = 0
8*A + 9*B + 4*C + 11*E + 11*E2 - 60*M2 = 0
5*A + 10*B + 7*C + 3*D + 3*D2 + 2*E + 2*E2 - 60*M3=0

D <= 20
E <= 20

M1 <= 128
M2 <= 128
M3 <= 128