Answer: Profit equation is [tex]y=58x - 7500[/tex]
Explanation:
[tex]Number of units sold= x[/tex]
[tex]Y = Profit [/tex]
[tex]Slope = \frac{Change in y}{change in X}[/tex]
[tex]\frac{6520 - 3520}{240 - 190}[/tex]
[tex]= \frac{2900}{50}[/tex]
[tex]= 58[/tex]
[tex]Y=mX+b[/tex]
[tex]Y= 58X+b[/tex]
Substituting the value of profit and units sold into this equation we can find out the value for b,
[tex]When y=6420 , x=240[/tex]
[tex]6420= 58(240) + b[/tex]
[tex]-7500=b[/tex]
So, the profit equation is[tex]y=58x - 7500[/tex]
The profit function will be [tex]\rm p = 58x - 7,500[/tex] , where x is the number of units sold and p is the profit. The given equation is obtained by substituting values in the equation to find slope that is:
[tex]\rm y = mx + b[/tex]
Given:
[tex]\rm Profit\: on \:sale \: of \: 190\: units = \$3,520\\\\\rm Profit\: on \:sale \: of \: 240\: units = \$6,420\\[/tex]
Therefore equations for both scenarios will be:
[tex]\rm \$3,520 = m(190) + b\\\\\rm \$4,420 = m(240) + b[/tex]
Let x be the number of units and p be the profit of the company.
Slope(m) will be calculated as:
[tex]\rm m = \dfrac{Change\:in\:profit}{Change\:in\;units}\\\\\rm m = \dfrac{\$6,240 - \$3,520}{240 - 190}\\\\\rm m = \dfrac{\$2,900}{50}\\\\m = 58[/tex]
Substituting the value of m in profit equation 1:
[tex]\rm \$3,520 = m(190) + b\\\\\rm \$3,520 = 58(190) + b\\\\\begin{aligned}\rm \$3,520 &= 11,020 + b\\\\b &= 11,020 - 3,520\\\\b &= 7,500\end[/tex]
Therefore the profit function will be:
[tex]\rm p = 58x - 7,500[/tex]
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