Lens Care Inc. (LCI) manufactures specialized equipment for polishing optical lenses. There are two models - one mainly used for fine eyewear (F-32) and another for lenses used in binoculars, cameras, and similar equipment (B-13). The manufacturing cost of each unit is calculated using activity-based costing, using the following manufacturing cost pools:

Cost Pools Allocation Base Costing Rate
Materials handling Number of parts $ 2.40 per part
Manufacturing supervision Hours of machine time $ 14.80 per hour
Assembly Number of parts $ 3.30 per part
Machine setup Each setup $ 56.50 per setup
Inspection and testing Logged hours $ 45.50 per hour
Packaging Logged hours $ 19.50 per hour

LCI currently sells the B-13 model for $1,775 and the F-32 model for $1,220. Manufacturing costs and activity usage for the two products are as follows:
B-13 F-32
Direct materials $ 164.50 $ 75.60
Number of parts 160 120
Machine hours 7.90 4.20
Inspection time 1.70 0.80
Packaging time 0.90 0.50
Setups 3 2

The market price for B-13 and F-32 are reduced to $1,695 and $1,095 respectively. To achieve the target cost, Lens Care plans to reduce materials handling costs. How many parts must be removed from B-13 in order to achieve the target cost for B-13 (round up to whole units)?

Multiple Choice
15
46
25
53
34

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

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1 x=22.52

2: 65/39=604+39x

65x-39x=604

26x=604

x=604/26

×=23.23

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step-by-step explanation: