Lingo Problem:

A company manufactures two products. If it charges price p₁ for product 1 and price p₂ for product 2, it can sell quantities q₁ = 60 3p₁ + p₂ and q₂ = 80 2p₂ + p₁ for products 1 and 2, respectively. It costs the company $5 to produce a unit of product 1 and $12 to produce a unit of product 2.

How many units of each product should the company produce? What prices should it charge, to maximize profit?

a. what was the total cost incurred for the optimum profit? (Enter your answer without using $-sign)

b. At the optimum, what was the net margin (i.e., the price minus unit cost) for Product 1?

c. At what cost for Product 2 would you only produce Product 1? Round your answer up to the nearest dollar. (HINT: plot demand for product 2 vs. cost of product 2 for costs of $12, $24, $36, and $48. When you determine the range of values when demand -> 0 start at the mid-point of the range and go up or down in increments of $1 until you get an answer)