ABCD company is an office equipment company that produces two types of desks: standard and deluxe. Deluxe desks have oak tops, more expensive hardware, and require additional time for finishing and polishing. Standard desks require $80$ square feet of pine and $10$ hours of labor, while deluxe desks require $60$ square feet of pine, $18$ square feet of oak, and $16$ hours of labor. For the next week, the company has $5,000$ square feet of pine, $750$ square feet of oak, and $400$ hours of labor available. Standard desks net a profit of $$150,$ while deluxe desks net a profit of $$320.$ All desks can be sold to national chains shops.

Instructions:

If the spreadsheet and Excel Solver results are given to you as follows $($see Table $1$ below$),$ address the following questions:

What are your Binding Constraints?

What is your Optimum profit $[$hint: maximized profit$]?$

What are your slack values for Pine, Oak, and Labor?

Looking at the Shadow prices, how much would the objective profit increase by if you were to increase labor hours by $50?$

If the optimum solution for standard desk stays the same, but deluxe desk numbers increased, what would be your estimated deluxe desks in this case? Would you recommend this option? Why? Hints: Notice that by increasing labor hours by $50,$ the S stays as an original optimum solution given in the information of Solver, but D will increase. The question is asking you to find how much the objective profit would go up and what would be the estimated number for D $[$calculated from your constraints. Decimal number is accepted$].$

What would be the changes in objective profit $$,$ if we increase the Pine by one unit and the Oak by one unit, i$.$e$.,$ Pine available$=5001$ and Oak available$=751.$

What $\%$ of available Oak can be reduced without it affecting the current $($given$)$ optimum solution?

What $\%$ of available Pine can be reduced without affecting the current $($given$)$ optimum solution?

How much should the standard desk unit profit of $$150$ be increased by in order for Standard desks to be produced $($i$.$e$.$ become a positive number$)?$

Given results after developing the excel LP and Solver:

Excel program

Standard

Deluxe

Availability

Pine

$80$

$60$

$5000$

Oak

$0$

$18$

$750$

Labor

$10$

$16$

$400$

Profit$/$unit

$$150$

$$320$

Number produced

$0$

$25\mathrm{.}0$

Total $($per week$)$

Profit contribution

$$0$

$$8,000$

$$8,000$

Amount Used

Pine

$1500$

Oak

$450$

Labor

$400$

Solver Sensitivity Report:

Variable Cells

Final

Reduced

Objective

Allowable

Allowable

Cell

Name

Value

Cost

Coefficient

Increase

Decrease

$B$$21$

Number produced Standard

$0$

$-50$

$150$

$50$

$1$E$+30$

$C$$21$

Number produced Deluxe

$25$

$0$

$320$

$1$E$+30$

$80$

Solver Constraints

Final

Shadow

Constraint

Allowable

Allowable

Cell

Name

Value

Price

R$.$H$.$ Side

Increase

Decrease

$B$$25$

Pine Amount Used

$1500$

$0$

$5000$

$1$E$+30$

$3500$

$B$$26$

Oak Amount Used

$450$

$0$

$750$

$1$E$+30$

$300$

$B$$27$

Labor Amount Used

$400$

$20$

$400$

$266\mathrm{.}6666667$

$400$