Question

1. Alexa is the manager of a business in Chicago which makes air conditioner. The business makes 1000 air conditioners a day in batches of 100, and Alexa has determined that the revenue function and cost function for air conditioners each day are:      R(p) = -2p² + 48p        C(p) = 6p + 200      

where p is a batch of 100 air conditioners, and R(p) and C(p) are in hundred dollars.

Due to the coronavirus, the business cam convert the factory to production of masks, and for masks, the revenue and cost function each day will be:   

R(f) = 52f                  C(f) =14f + 150

where f is a batch of 100 masks, and R(f) and C(f) are in hundred dollars.

Due supply of materials, the business will only be able to make air conditioners and masks in batches of 100, and the total capacity will still be 1000 total products/day.

1. To maximize the total profit, how many batches of air conditioners and how many batches of masks should the business manufacture?

2. What is the maximum daily profit?

Answer 1

total profit for maximum total air conditioner let batches 'P' and masks for batches produced be f. the produced be 1 Air conditioner Profit Revenue Cost function Profit = (-2p²+486)-(Ep+200) Profit, -2p²+420-200 - 0 e Masks Cost price - pro fit = Revenue - 52f (14f+ 150) Profita = 38f-1 . 150 Total profit = Profit, + Profita - 2p+420-200 +38f- T = . 150 Given in one produced, so I batch = day 1000 Total products are 100 product 10 batches are manufacture hence in one day

To maximise profit; I batch of air conditioner and 9 batches of mask are manufactured maximum daily profit = .-2p?+4pt 30 p = T = -2(1) +4 +30 T=32 - maximum daily Profit