The cost function for a certain company is&nbsp;C=60x+300&nbsp;and the revenue is given by&nbsp;R=100x−0.5x2. Remember that revenue less cost equals profit. Find two values of x (production level) in a quadratic equation that will result in a profit of&nbsp;$300.

Question

The cost function for a certain company is&amp;nbsp;C=60x+300&amp;nbsp;and the revenue is given by&amp;nbsp;R=100x−0.5x2. Remember that revenue less cost equals profit. Find two values of x (production level) in a quadratic equation that will result in a profit of&amp;nbsp;$300.

Sarythe · Accepted Answer

Step 1  Given:  C=60x+300  R=100x−0.5x2  Profit =$300, solve for x.  We know that:  Profit =R−C  Step 2  Then,  300=(100x−0.5x2)−(60x+300)  300=100x−0.5x2−60x−300  300=−0.5x2+40x−300  0.5x2−40x+300+300=0  0.5x2−40x+600=0  12x2−40x+600=0  x2−80x+12002=0  x2−80x+1200=0  x2−60x−20x+1200=0  x(x−60)−20(x−60)=0  (x−60)(x−20)=0  x=20, 60  So final as:  The two values of x are 20 and 60

nick1337 · Accepted Answer

Answer:x=20 and x=60Explanation:Profit is calculated by subtracting the cost from the revenue:P=R−CGiven that the cost function is C=60x+300 and the revenue function is R=100x−0.5x2, we can substitute these expressions into the profit equation:P=(100x−0.5x2)−(60x+300)Simplifying this equation, we have:P=100x−0.5x2−60x−300Combining like terms:P=−0.5x2+40x−300We want to find the values of x that make the profit P equal to 300. Therefore, we set up the equation:−0.5x2+40x−300=300Rearranging the equation, we get:−0.5x2+40x−600=0This is a quadratic equation in standard form. To find the values of x that satisfy this equation, we can use the quadratic formula:x=−b±b2−4ac2aIn our case, the quadratic equation is:−0.5x2+40x−600=0Comparing this equation to the standard quadratic equation form, we can determine the values of a, b, and c:a=−0.5, b=40, and c=−600Substituting these values into the quadratic formula, we get:x=−40±402−4(−0.5)(−600)2(−0.5)Simplifying further:x=−40±1600−1200−1x=−40±400−1x=−40±20−1Hence, we have two possible values for x:x1=−40+20−1=20x2=−40−20−1=60Therefore, the production levels that result in a profit of 300 are x=20 and x=60.

Vasquez · Accepted Answer

Step 1:The cost function is given as C=60x+300, and the revenue function is given as R=100x−0.5x2.The profit function is defined as P=R−C. Substituting the given cost and revenue functions, we have:P=(100x−0.5x2)−(60x+300).To find the values of x that result in a profit of 300, we set up the following equation:300=(100x−0.5x2)−(60x+300).Simplifying the equation, we have:0.5x2−40x+600=0.Step 2:Now we have a quadratic equation. To solve it, we can use the quadratic formula:x=−b±b2−4ac2a.Comparing the equation 0.5x2−40x+600=0 to the general form ax2+bx+c=0, we have:a=0.5, b=−40, and c=600.Step 3:Substituting these values into the quadratic formula, we get:x=−(−40)±(−40)2−4(0.5)(600)2(0.5).Simplifying further:x=40±1600−12001.x=40±4001.x=40±201.Thus, the two values of x (production levels) that will result in a profit of 300 are:x=20 and x=60.

The cost function for a certain company is C= 60x+300

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