$($please help me solve this questions$)$ Suppose that the post office can force employees to work one day of overtime each week. For

example, an employee whose regular shift is Monday to Friday can also be required to work on

Saturday. Each employee is paid $$50$ a day for each of the first five days worked during a week

and $$62$ for the overtime day $($if any$).$ Formulate an LP whose solution will enable the post office

to minimize the cost of meeting its weekly work requirements.

Question $4$:

Bullco blends silicon and nitrogen to produce two types of fertilizers. Fertilizer $1$ must be at least

$40\%$ nitrogen and sells for $$70//$lb$.$ Fertilizer $2$ must be at least $70\%$ silicon and sells for $$40//1$b$.$

Bullco can purchase up to $801$ b of nitrogen at $$15//$lb and up to $1001$ lb of silicon at $$10//$lb$.$ Assuming

that all fertilizer produced can be sold, formulate an LP to help Bullco maximize profits.

Question $5$:

James Beerd bakes cheesecakes and Black Forest cakes. During any month, he can bake at most

$65$ cakes. The costs per cake and the demands for cakes, which must be met on time are listed in

the following Table. It costs $$0\mathrm{.}5$ to hold a cheesecake, and $$0\mathrm{.}4$ to hold a Black Forest cake, in

inventory for a month. Formulate an LP to minimize the total cost of meeting the next three

months' demands.