Solve the following LP using the Excel solver, your work should include the main sheet and the answer sheet. Uploaded it as a file.

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Decision Variables

$x_{ij}=$ number of tons of cargo type $i=1,2,3,4$ stored in compartment $j=F($Front$),$ C $($Center$),$ B $($Back$).$

The linear program is as follows:

Maximize $P=320(x_{1F}+x_{1C}+x_{1B})+400(x_{2F}+x_{2C}+x_{2B})$

$+360(x_{3F}+x_{3C}+x_{3B})+290(x_{4F}+x_{4C}+x_{4B})$

S$.$t$.$

$x_{1F}+x_{2F}+x_{3F}+x_{4F}12$

$x_{1C}+x_{2C}+x_{3C}+x_{4C}18$

$x_{1B}+x_{2B}+x_{3B}+x_{4B}10$

$x_{1F}+x_{1C}+x_{1B}20$

$x_{2F}+x_{2C}+x_{2B}16$

$x_{3F}+x_{3C}+x_{3B}25$

$x_{4F}+x_{4C}+x_{4B}13$

$500x_{1F}+700x_{2F}+600x_{3F}+400x_{4F}7,000$

$500x_{1C}+700x_{2C}+600x_{3C}+400x_{4C}9,000$

$500x_{1B}+700x_{2B}+600x_{3B}+400x_{4B}5,000$

All $x_{ij}0$