Question

Production Man Hours You make 3 models of a drill press, the A-1237, the A-1322, and the A- 1481. The A-1237 requires 1.6 hours to paint, 3 hours to assemble, and .25 hours to package. The A-1322 takes 1.5 hours to paint, 2.8 hours to assemble, and .3 hours to package. The A-1482 takes 1.4 hours to paint, 3.1 hours to assemble, and .28 hours to package. You have workers so that there are 565 man-hours per day to paint, 1092.5 man-hours per day to assemble, and 106 man-hours per day to package. If every man-hour is to be used, then how many of each model should be produced? 1.

explain steps thanks

Answer 1

Let x denote A-1237, y denote A-1322 and z denote A-1481. Then in matrix form we can write the system of equations required to solve in order to find the number of each model produced as

$\begin{bmatrix} 1.6 & 1.5& 1.4\\ 3 & 2.8 & 3.4\\ 0.25 & 0.3 & 0.28 \end{bmatrix} \begin{bmatrix} x\\ y\\z \end{bmatrix}= \begin{bmatrix} 565\\ 1092.5\\106 \end{bmatrix}$

Which gives

$\begin{bmatrix} x\\ y\\z \end{bmatrix}= \begin{bmatrix} 1.6 & 1.5& 1.4\\ 3 & 2.8 & 3.4\\ 0.25 & 0.3 & 0.28 \end{bmatrix}^{-1} \times \begin{bmatrix} 565\\ 1092.5\\106 \end{bmatrix}$

Using MATLAB for the calculations we get

Thus approximately 100 of model A-1237, 227 of model A-1322 and 46 of model A-1481 must be produced