Programming Models and Contribution Per Unit - Essay Example

?Task 1. Contribution per unit Contribution per unit is calculated in order to form an objective function. The variable cost per hour for each testdevice is multiplied by the number of hours required for testing each peripheral device on a particular test device. Firstly, the total labor cost per unit for each peripheral device can be calculated by adding up the variable labor cost per unit for each test device. After this, total cost is calculated by adding the variable labor cost and material cost. The difference of selling price per unit and total cost per unit gives contribution per unit for each peripheral device. The contribution per unit received for Internal Modem, External Modem, Circuit Board, CD Drive, Hard Drive and Memory Board are 156.82, 156.10, 250.87, 167.90, 290.78 and 274.22 respectively. 2. Formulation of linear programming model The linear programming model can be developed by forming equations for constraints and objective functions. The equations for constraints are formed using the available time on each testing device. These equations are: 2IM+3EM+5CB+6CD+4HD+8MB= 224 gm 2. Optimum Solution The linear programming model is solved using excel solver. The optimum solution for daily intake can be derived from either of the answer or sensitivity reports as follows: BR =2 CH =0 CO= 1 PC =1 3. Optimum value of objective function The objective function at the optimal values of each variable is calculated by inserting these values in the equation for objective function as: Objective function = .85*2 + 1.25*0 +.75*1 + 1.15*1 = 3.6 This implies that this is the minimum value of output which the client has to take to fulfill the constraints of calorie intake. 4. Surplus/Slack The answer report depicts that chocolate, sugar and fat were fully utilized as the surplus/slack is 0. The calorie intake is not fully utilized i.e. it is not binding. 5. Surplus value There is a surplus in the calorie intake which can be calculated as (1096.19 – 550) i.e. 546.19 calories 6. Impact of change in unit price If the unit price for pineapple cheese cake increase to ?1.5, the optimal solution would change and the objective function would increase to 3.95 (3.6 + (1.50 – 1.15)). The allowable increase in this case is .55 as seen from sensitivity report. Since the increase of .35 is within this limit, the objective function would increase by .35. 7. Shadow Price Shadow price can be defined as the change in the value of objective function obtained in optimal solution by relaxing or tightening a constraint by 1 unit. For example, if daily sugar intake is increased by 1 gm, the objective function increases by ?.0067. 8. Summary & Recommendations The client’s constraints and objectives have been derived from the answer reports available. The decision variables are the number of brownies, chocolate ice creams, colas and pineapple cheese cakes. The optimal solution obtained depicts that the client should not consume any chocolate ice-cream. It can be seen that 3 variables have been fully utilized while there is a surplus in the calorie intake. This surplus is a must to fulfill other constraints unless they are relaxed. The minimum value of objective function is 3.6. The shadow prices help in determining the impact of increasing or decreasing a constraint on the objective. It can be noticed that relaxing the constraint of daily sugar intake has maximum impact on objective function. This is followed by chocolate intake and fat intake. Relaxing constraint for calorie intake has no impact since it is already over-utilized. Therefore, sugar intake should be preferred to achieve overall objective. References Hamdy A. Taha 2008, ‘Operations Research: An Introduction’, 8th Edition Read More