3.4.1 A single line

These questions all refer to the above production time function introduced at the beginning of this class, and given by the formula

$$\fbox{$H = 50 + 0.25 \times I,$ }$$

Each question will be translated into a generic statement in order to understand its essence.

How long will it take to produce 145 units?

Generic: given an x, what's the value of y?

This amounts to simply plugging in the value of x = 145 to the equation:

$$\fbox{$y = 50 + 0.25 \times x,$ }$$

giving

$$\fbox{$y = 50 + 0.25 \times 145,$ }$$

so that y equals 86.25.

I need as many as you can produce, but I can't wait more than 3 days.

Generic:Given a value of y, what must x be?

In this example, y is forced to be 72 (3 days - it's a 24 hour a day production process), so we solve the straight line equation for x,

$$\fbox{$72 = 50 + 0.25 \times x.$ }$$

Rearranging this gives

$$\fbox{$72 - 50 = 0.25 \times x,$ }$$

so

$$\fbox{$22 = 0.25 \times x,$ }$$

which means that

$$\fbox{$\frac{22}{0.25} = x,$ }$$

indicating that x = 88, so the client can get 88 items within 3 days.