how many units of each should be manufactured to maximize income?

Question

A manufacturer is producing two types of units. Each unit Q costs $9 for parts and $15 for labor and each unit R costs $6 for parts and $20 for labor. The manufacturer's budget is $810 for parts and $1800 for labor. If the income per unit is $150 for Q and $175 for R, how many units of each should be manufactured to maximize income?

Answer 1

A solution to this question can be done as follows:

 

Q units cost $9 for parts and $15 for labor, or $24 cost/unit

R units cost $10 for parts and $20 for labor, or $26 cost/unit

 

the sale price of Q units is $150, so the per unit income is $150 - 24 = $126/unit

 

the sale price of R units is $175, so the per unit income is $175 - 26 = $149/unit

 

Based on that analysis, the manufacturer should build ONLY R units. Combining Q and R units will result is a lesser income.