Shows the hourly cost of four types of manufacturing processes. It also shows the number of hours required of each process to produce three different products. Use matrices and MATLAB to solve the following. (a) Determine the cost of each process to produce one unit of product I. (b) Determine the cost to make one unit of each product

(c) Suppose we produce 10 units of product 1,5 units of product 2, and 7 units of product 3. Compute the total cost

Cost and time data for manufacturing processes

Solution

(a) The basic principle we can use here is that cost equals the hourly cost t~’the number of hours required. For example, the cost of using the lathe for product I is ($10/h)(6 h = $60, and so forth for the other three processes. If we define the row vector of h costs to be hourly_costs and define the row vector of hours required for p
I to be hours_I, then we can compute the costs of each process for product I element-by-element multiplication. In MATLAB the session is

These are the costs of each of the four processes to produce one unit of product I.

(b) To compute the total cost of one unit of product I, we can use the vectors hourly _cos t s and hours_l but apply matrix multiplication instead of element-by element mutiplication, because matrix multiplication sums the individual products. The matrix multiplication gives

We can perform similar multiplication for products 2 and 3, using the data in the table. For product 2:

These three operations could have been accomplished in one operation by defining a matrix whose columns are formed’ In!. die data in the last three columns of the table:

In MATI..AB the session continues as follows. Remember that we must use the transpose operation to convert the row vectors into column vectors.

Thus the costs to produce one unit each of products I, 2, and 3 is $162, $114,and $149,respectively. (c) To find the total cost to produce 10,5, and 7 units, respectively, we can use matrix multiplication:

In MATLAB the session continues as follows. Note the use of the transpose operator on the vector uni t_cost.
»units = [10, 5, 7]; »tota1_cost units*unit_cost’
total_cost = 3233
The total cost is $3233.