Question

A company invests $14,000 to produce a product that will sell for $63.80 each. Each unit costs $9.40 to produce. Let C represent the total cost in dollars of producing x units. Write an equation for C in terms of x. C = Let R represent the revenue in dollars when x units are produced. Write an equation for R in terms of X. R= Let P represent the profit in dollars when x units are produced. Write an equation for Pin terms of x. Note profit is given by revenue minus cost. P= (a) How many units must the company sell to break even? (Round to the nearest whole unit.) units (b) How many units must the company sell to make a profit of $110,000? (Round to the nearest whole unit.) units

Answer 1

To write the equations C, R, and P in terms of x, we can consider the cost, revenue, and profit per unit. Then, we can solve for the number of units required to break even or make a specific profit.

Step-by-step explanation:

To write an equation for C in terms of x, we need to consider that the total cost (C) is equal to the cost per unit (9.40) multiplied by the number of units produced (x), so the equation is C = 9.40x.

To write an equation for R in terms of x, we know that the revenue (R) is equal to the selling price per unit (63.80) multiplied by the number of units produced (x), so the equation is R = 63.80x.

To write an equation for P in terms of x, we can substitute C and R into the equation for profit (P), which is given by P = R - C. Substituting the equations for C and R, we get P = (63.80x) - (9.40x).

(a) To break even, the company's profit (P) should be zero. So, we can set the equation 0 = (63.80x) - (9.40x) and solve for x.

(b) To make a profit of $110,000, we can set the equation 110,000 = (63.80x) - (9.40x) and solve for x.

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