Question

2. A manufacturer produces two models of a certain product: model A and model B. There is a R20 profit on model A and an R35 profit on model B. Three machines M1,M2 and M3 are used jointly to manufacture these models. The number of hours that each machine operates to produce 1 unit of each model is given in the table: Model A Model B Machine M1 1 1 2 1 Machine M2 3 4 1 1 2 Machine M3 1 1 3 1 1 3 No machine is in operation more than 12 hours per day. Now let x be the number of model A made per day and y be the be the number of model B made per day. Then x and y satisfies the following constrains

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c} & Model\ A & Model\ B \\ \hline Machine\ 1 & 3/2 & 1 \\ \hdashline Machine\ 2 & 3/4 & 3/2 \\ \hdashline Machine\ 3 & 4/3 & 4/3 \\ \end{array}$$

Let $x$ be the number of model A made per day: $x\geq0.$

Let $y$ be the be the number of model B made per day: $y\geq0.$

Machine 1 is in operation more than 12 hours per day:

$$\dfrac{3}{2}x+y\leq12$$

Machine 2 is in operation more than 12 hours per day:

$$\dfrac{3}{4}x+\dfrac{3}{2}y\leq12$$

Machine 3 is in operation more than 12 hours per day:

$$\dfrac{4}{3}x+\dfrac{4}{3}y\leq12$$

The answer is:

$$x\geq0, y\geq0,\dfrac{3}{2}x+y\leq12,$$

$$\dfrac{3}{4}x+\dfrac{3}{2}y\leq12, \dfrac{4}{3}x+\dfrac{4}{3}y\leq12$$