Answer to Question #274852 in Calculus for sumu

Question

6. A company manufacturing wicker baskets knows that it has variable costs of $0.62 per unit and fixed costs of $150 per week. Its baskets sell for $2.40 each. Assuming that total costs are a linear function of output, calculate the level of weekly sales necessary to:

(i) Break-even

(ii) Reach a profit of $4300 per week

Answer 1

Let $x=$ the number of wicker baskets produced per week. Then the total cost will be

$$TC(x)=0.62x+150$$

$$TR(x)=2.40x$$

The profit will be

$$P(x)=2.40x-(0.62x+150)$$

$$P(x)=1.78x-150$$

(i)

$$P=0=>1.78x-150=0$$

$$x=84$$

The level of weekly sales is $84$ wicker baskets.

(ii)

$$P=4300=>1.78x-150=4300$$

$$x=2500$$

The level of weekly sales is $2500$ wicker baskets.