A consumer electronics company makes two different types of smart phones, the j8 and the j8+. Suppose that j9 corresponds to a new smart pho
A consumer electronics company makes two different types of smart phones, the j8 and the j8+. Suppose that j9 corresponds to a new smart phone produced by the company. The manufacturing cost includes labor, materials, and overhead (facilities, etc.). The company’s costs (in dollars) per unit for each type are summarized in the following table.
j8 j8+ j9
Labor 57 73 81
Materials 93 101 113
Overhead 29 34 38
a. Suppose T is the linear transformation that takes as input a vector of unit counts for j8’s, j8+’s, and j9’s respectively, and produces for output a vector of total labor, material, and overhead, respectively. Find a formula for T. (A graphing calculator is recommended.)
b. Determine T −1, and use it to find the production level for each type of phone that will result in the given costs.
Labor = $1955, Materials = $2815, Overhead = $931
(j8, j8+, j9) = ???