Gastineau Corporation's two products have the following characteristics: The constrained resource is a particular machine that is available for 9, 600 minutes each month.Each unit of product J45Z requires 19 minutes on this machine and each unit of product W47E requires 7 minutes on this machine. How many units of product J45Z should be produced each month?

Question

Gastineau Corporation's two products have the following characteristics:  The constrained resource is a particular machine that is available for 9, 600 minutes each month.Each unit of product J45Z requires 19 minutes on this machine and each unit of product W47E requires 7 minutes on this machine. How many units of product J45Z should be produced each month?

Quizplus · Accepted Answer

We need to find the number of units of product J45Z that should be produced each month. Let's assume x units of J45Z are produced in a month.
So the time required by x units of J45Z on the machine = 19x minutes.
Similarly, the time required by y units of W47E on the machine is 7y minutes.
As the machine is available for 9,600 minutes each month, we can write the following equation:
19x + 7y ≤ 9600
We need to maximize the production of J45Z. So, we need to find the maximum value of x that satisfies the above equation.
To do that, we can use trial and error, or we can solve for y and get an equation in terms of x to plot on a graph.
Let's solve for y:
7y ≤ 9600 - 19x
y ≤ (9600 - 19x) / 7
So the equation for the line representing the maximum value of y is y = (9600 - 19x) / 7.
Plotting this on a graph and finding the point where the line intersects the x-axis, we get x = 170.
So, the maximum number of units of J45Z that can be produced while staying within the time constraint is 170. Therefore, the answer is C (170 units).

Gastineau Corporation's Two Products Have the Following Characteristics: the Constrained