Delta company produces a single product. the cost of producing and selling a single unit of this product at the company's normal activity level of 104,400 units per year is: direct materials $ 2.20 direct labor $ 4.00 variable manufacturing overhead $ .90 fixed manufacturing overhead $ 4.45 variable selling and administrative expenses $ 1.80 fixed selling and administrative expenses $ 3.00 the normal selling price is $19 per unit. the company's capacity is 133,200 units per year. an order has been received from a mail-order house for 2,400 units at a special price of $16.00 per unit. this order would not affect regular sales. required: 1. if the order is accepted, by how much will annual profits be increased or decreased? (the order will not change the company's total fixed costs.)

Since we want to solve for the variable x, we want to isolate x

a²x + (a - 1) = (a + 1)x ⇒ Distribute x to (a+1). Also, remove parentheses

a²x + a - 1 = ax + x ⇒ Subtract a from both sides

a²x - 1 = ax + x - a ⇒ Add 1 to both sides

a²x = ax + x - a + 1 ⇒ Subtract (ax + x) from both sides

a²x - (ax + x)= ax + x - a + 1 - (ax+x) ⇒ Simplify. Remember that multiplying positive by negative = negative

a²x - ax - x = ax + x - a + 1 - ax - x ⇒ Simplify

a²x - ax - x = -a + 1 ⇒ Factor out the x from a²x - ax - x

x(a² - a - 1) = -a + 1 ⇒ Divide both sides by (a² - a - 1)

x = (-a + 1) / (a² - a - 1)

However, we need to make sure that the denominator does not equal 0. Therefore, you set the denominator = 0 (just use the quadratic formula for this), and it gives that the denominator =0 when a = (1+√5)/2 AND (1-√5)/2

Therefore, the final answer is

x = (-a + 1) / (a² - a - 1) given that a ≠ (1+√5)/2, a ≠ (1-√5)/2