Team assignment - Essay Example

Team Assignment #48 A furniture company produces three types of desks: a children’s model, an office model, and a deluxe model. Each desk is manufactured in three stages: cutting, construction, and finishing. The time requirements for each model and manufacturing stage are given in the following table.Each week the company has available a maximum of 100 hours for cutting, 100 hours for construction, and 65 hours for finishing. If all available time must be used, how many of each type of desk should be produced each week?

Solution Let the furniture company produces each type of desk per week as below: x - number of children’s modely - number of office modelz - number of deluxe modelThe given time constraint for cutting, construction, and finishing for each type of model can be summarized as below:Cutting : (Equation 1)Construction : (Equation 2)Finishing : (Equation 3)The above equations are Linear Equations in three variables.Step 1: Reducing the system to two Equations in two variables.Let’s eliminate x from Equations 1 and 2.

Multiplying equation 3 by 2 and then subtracting equation 1 from it. (Equation 4)Multiplying Equation 3 by 2 and then subtracting equation 2 from it. (Equation 5)Equations 4 and 5 give us a system of two Equations in two variables.Step 2: Solve the resulting system of two Equations in two variables.Using addition method to solve Equations 4 and 5 for y and z. Adding Equations 4 and 5. Step 3: Back-substituting the value of z in equation 5. Step 4: Back substituting the values of y and z in equation 3.

With x = 15, y = 10, and z = 20, the proposed solution is the ordered triple (15, 10, 20).Step 5: Checking the proposed solution, by substituting the values for x, y, and z into each of the three original equations. These substitutions yield three true statements. Thus, the solution is (15, 10, 20) and the solution set is (15, 10, 20).If all available time must be used, the furniture company should produce each week 15 children’s model desks, 10 office model desks, and 20 deluxe model desks.

In practical, the main consideration is profit contribution from each type of desk. Therefore, the time constraint for three stages cutting, construction, and finishing must be allocated in such a way so that company realizes maximum profit. However, in given case, the profit contribution from each type of desk is not given; therefore, the time should be allocated in such a way so that all the available time must be used.