A furniture manufacturer produces chairs. It costs R2 200 to manufacture 100 chairs in one day, and R4800 to?
A furniture manufacturer produces chairs. It costs R2 200 to manufacture 100 chairs in one day, and R4800 to manufacture 300 chairs in one day. Suppose the relationship between cost and number of chairs produced is linear and we represent the relationship by means on an equation. Which of the following statements is/are true?
A. An equation that expresses this relationship is y= 13x +900 , where x represents the number of chairs produced each day, and y represents the cost per day.
B. The y-intercept of the line represented by this equation indicates the fixed daily cost of operating the factory.
C. It costs R4400 to make 200 chairs.
1. Only A
2. Only B
3. Only C
4. Only A and B
5. Only B and C
Tagged with: 13x • chairs • furniture manufacturer • r2 • relationship • y intercept
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A. is true because 13*100+900=2200 and 13*300+900=4800
B. is true, the y-intercept is when x=0, i.e. when you produce nothing, which gives the fixed daily operating cost
C. is not true, because due to A. the equation is given by y=13*x+900 and then to make 200 chairs it will cost 13*200 + 900 = 3500
Thus 4. Only A and B is the correct answer.
Test statement A by plugging in values:
2200 = 13 * 100 + 900
2200 = 1300 + 900…TRUE
4800 = 13 * 300 + 900
4800 = 3900 + 900…TRUE
Statement A is TRUE.
The y-intercept is where the line touches the y-axis. In other words, the y-intercept is the y-value when x = 0. When x = 0, that means no chairs are made, but there is still an associated cost:
y = 13 * 0 + 900
y = 900
Statement B is TRUE.
To test statement C, since we know statement A is true, just plug in 4400 and 200:
4400 = 13 * 200 + 900
4400 = 2600 + 900
4400 = 3500…FALSE
Statement C is FALSE.
The correct answer is 4. Only A and B.