Q$6$ IKEA is exploring two machines to produce adjustable table

legs, which have been in high demand since the launch of online

classes after the outbreak of Covid$-19.$ The first machine $($say A$)$

would cost $$24000$ and incurs a variable cost of $$20$ per leg. The

second machine $($say B$),$ costing $$29325,$ and the variable cost

per leg is only $$15.$ Each leg made from machine A needs a

scratch$-$proof bottom bush which costs $$0\mathrm{.}50.$ The furniture store

sells each leg at $$50$ to the customers.

a$)$ What is the breakeven volume for machine A$?$ Also, find

the breakeven point in dollars.

b$)$ What is the breakeven volume for machine B$?$ Also, find

the breakeven point in dollars.

c$)$ If the store expects a sale of $900$ legs, which machine $($A or

B$)$ will you choose? Also, provide the 'opportunity loss' if

the furniture store does not determine the better machine.

d$)$ If the breakeven volume of $A$ is $900$ legs, what price

should A charge for each leg?

e$)$ Find the volumes of both processes such that A has $1500$

legs less than B$,$ and the profit is $$59925$ less than B$.$Q$1.$ Carrefour wants to launch its brand of in$-$store$-$grown

organic lettuce in small bags. The supermarket has two options

for processing harvested lettuce: manual processing $($say A$)$ and

mechanized processing $($say B$).$ The manual process will incur a

monthly processing cost of $$1500$ and a variable cost of $$2$ per

bag, while the mechanized process will incur a monthly

processing cost of $$1040$ and a variable cost of $$1\mathrm{.}50$ per bag.

Besides, the mechanized process needs a recyclable bag costing

$$\frac{0\mathrm{.}25}{?}$ bag to Carrefour. The store expects to fix the price at $$5$

per bag, irrespective of the processes.

a$)$ What is the breakeven volume for the manual process?

Also, find the breakeven point in dollars.

b$)$ What is the breakeven volume for the mechanized

process? Also, find the breakeven point in dollars.

c$).$ Which process will you use if you expect sales of $600$

bags monthly? Also, provide the opportunity loss of profit

if the store does not determine the better method.

d$)$ At what sales volume is the profit from the sales made

from the mechanized process more than the profit from the

sales made from the manual process by $$710?$

e$)$ Find the bags of sales both processes such that the manual

method has $500$ bags more than the mechanized method,

and the profit of the mechanized process is $$790$ less than

the manual process.