A manufacturer of radios estimates that his daily cost of producing x radios is given by the equation C=350+5x. The equation R=25x represents the revenue in dollars from selling x radios.
*Profit function,P(x)=R(x)-C(x),P(x)=20x-350
*How many radios should the manufacturer produce and sell to have a daily profit of $500?
Tommy earns $18 an hour working for American Greetings. How much would Tommy need to earn on his own for a comparable income?
To find out how many radios should the manufacturer produce and sell to have a daily profit of $500, we can set the profit function equal to $500 and solve for x.
The profit function is given by P(x) = R(x) - C(x), where P(x) represents the profit, R(x) represents the revenue, and C(x) represents the cost.
Given that the profit function is P(x) = 20x - 350, we can set it equal to $500:
20x - 350 = 500
To isolate x, we can add 350 to both sides of the equation:
20x = 500 + 350
20x = 850
Next, divide both sides of the equation by 20 to solve for x:
x = 850 / 20
x = 42.5
Therefore, the manufacturer should produce and sell approximately 42.5 radios to have a daily profit of $500. Since you cannot sell half a radio, the manufacturer would round up to the nearest whole number. So, they should produce and sell 43 radios.