If c(x) is the cost of manufacturing an amount x of a given product and $10 is the price per unit amount, then the profit p(x) obtained by selling an amount x is p(x) = 10 x − c(x). (notice that there is a loss if p(x) is negative.) a. if c(x) = cx and c < 10, is there a maximum profit?

Bandar industries berhad of malaysia manufactures sporting equipment. one of the company’s products, a football helmet for the north american market, requires a special plastic. during the quarter ending june 30, the company manufactured 35,000 helmets, using 22,500 kilograms of plastic. the plastic cost the company $171,000. according to the standard cost card, each helmet should require 0.6 kilograms of plastic, at a cost of $8 per kilogram. 1. what is the standard quantity of kilograms of plastic (sq) that is allowed to make 35,000 helmets? 2. what is the standard materials cost allowed (sq x sp) to make 35,000 helmets? 3. what is the materials spending variance? 4. what is the materials price variance and the materials quantity variance?