Production data for the number of hours required per unit for making the Droid and iPhone versions of cell phone components by Bizzer, a high-tech manufacturing firm, is given below.Suppose the plant decides to make the maximum number of iPhone components possible and reach the rest of its capacity by making Droid phones.How many of each type of phone will it make?

Monthly Product

A)375 iPhone units and 625 Droid units
B)500 iPhone units and 500 Droid units
C)1000 iPhone units and 1000 Droid units
D)625 iPhone units and 375 Droid units

Question

Production data for the number of hours required per unit for making the Droid and iPhone versions of cell phone components by Bizzer, a high-tech manufacturing firm, is given below.Suppose the plant decides to make the maximum number of iPhone components possible and reach the rest of its capacity by making Droid phones.How many of each type of phone will it make?

Monthly Product

Monthly Product

A)375 iPhone units and 625 Droid units 
B)500 iPhone units and 500 Droid units 
C)1000 iPhone units and 1000 Droid units 
D)625 iPhone units and 375 Droid units

Quizplus · Accepted Answer

To maximize the production of iPhone components, we need to allocate as many hours as possible to making iPhones while still meeting the demand for Droids. We can find the maximum number of iPhone components by finding the intersection point of the two demand lines (assuming that the plant has a capacity to meet the demand for both types of components).

The equation for the demand line for iPhone components is:
y = -0.8x + 800

The equation for the demand line for Droid components is:
y = -x + 1000

where x is the number of hours spent making iPhone components and y is the number of hours spent making Droid components.

To find the intersection point, we need to solve for x and y:
-0.8x + 800 = -x + 1000
0.2x = 200
x = 1000

Substituting into either of the demand equations gives us the number of hours needed to make Droid components:
y = -x + 1000
y = -(1000) + 1000
y = 0

So we can make a maximum of 1000/1.6 = 625 iPhone components and the rest of the capacity will be used to make Droid components. Therefore, the plant will make 625 iPhone units and 375 Droid units.

Production Data for the Number of Hours Required Per Unit