Daniel is printing out copies of a presentation. It takes 3 minutes to print a color copy and 1 minute to print a black-and-whit
e copy. He needs to print at least 6 copies and must have the copies completed in no more than 12 minutes.
If the solution region represents the number of color copies and black-and-white copies that Daniel can print, determine which graph represents the solution set to the system of inequalities representing this situation.
If the solution region represents the number of color copies and black-and-white copies that Daniel can print, determine which graph represents the solution set to the system of inequalities representing this situation.
1 answer:
Utilize the details to create inequalities that reflect each limitation or requirement.
2) Label the variables.
c: count of color copies
b: count of black-and-white copies
3) Define each constraint:
i) <span>Printing a color copy requires 3 minutes while a black-and-white copy takes 1 minute.
</span><span>
</span><span>3c + b
</span><span>
</span><span>
</span><span>ii) He must print a minimum of 6 copies ⇒ c + b ≥ 6
</span><span>
</span><span>
</span><span>iv) Moreover, he must finish the prints within 12 minutes at most ⇒</span>
3c + b ≤ 12
<span />
4) Additional limits include c ≥ 0, and b ≥ 0 (meaning only non-negative counts are valid for each type of copy)
5) Here’s how to illustrate that:
i) For 3c + b ≤ 12: draw the line representing 3c + b = 12 and shade the area above and to the right of this line.
ii) For c + b ≥ 6: draw the line c + b = 6 and shade the area below and to the left of this line.
iii) Given that c ≥ 0 and b ≥ 0, the relevant region is located in the first quadrant.
iv) The concluding area is the overlap of the previously mentioned shaded regions.
v) The graph can be viewed in the attached figure.
2) Label the variables.
c: count of color copies
b: count of black-and-white copies
3) Define each constraint:
i) <span>Printing a color copy requires 3 minutes while a black-and-white copy takes 1 minute.
</span><span>
</span><span>3c + b
</span><span>
</span><span>
</span><span>ii) He must print a minimum of 6 copies ⇒ c + b ≥ 6
</span><span>
</span><span>
</span><span>iv) Moreover, he must finish the prints within 12 minutes at most ⇒</span>
3c + b ≤ 12
<span />
4) Additional limits include c ≥ 0, and b ≥ 0 (meaning only non-negative counts are valid for each type of copy)
5) Here’s how to illustrate that:
i) For 3c + b ≤ 12: draw the line representing 3c + b = 12 and shade the area above and to the right of this line.
ii) For c + b ≥ 6: draw the line c + b = 6 and shade the area below and to the left of this line.
iii) Given that c ≥ 0 and b ≥ 0, the relevant region is located in the first quadrant.
iv) The concluding area is the overlap of the previously mentioned shaded regions.
v) The graph can be viewed in the attached figure.
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